Question 1

Simplify the expression. Assume all variables represent positive real numbers.
- (−7) 66\sqrt [ 6 ] { ( - 7 )  ^ { 6 } }6(−7) 6​

Accepted Answer

A)    −7- 7−7 
B)   49
C)   not a real number
D)   7

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
- 483−333+39\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }348​​−333​​+9​3​​

Accepted Answer

A)    233\frac { 2 \sqrt { 3 } } { 3 }323c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    433\frac { 4 \sqrt { 3 } } { 3 }343c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    −453- \frac { \sqrt { 45 } } { 3 }−345c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    239\frac { 2 \sqrt { 3 } } { 9 }923c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​

Question 3

Decide whether the expression has been simplified correctly.
- 50x=x5 ^ { 0 } x = x50x=x

Accepted Answer

A)   Not simplified correctly
B)   Simplified correctly

Question 4

Factor out the greatest common factor. Simplify the factors, if possible.
- 5t2−10t−255 t ^ { 2 } - 10 t - 255t2−10t−25

Accepted Answer

A)    5t(t2−2t−5) 5 t \left( t ^ { 2 } - 2 t - 5 \right) 5t(t2−2t−5)  
B)    5(t2−2t−5) 5 \left( t ^ { 2 } - 2 t - 5 \right) 5(t2−2t−5)  
C)    5(t2−5t−20) 5 \left( t ^ { 2 } - 5 t - 20 \right) 5(t2−5t−20)  
D)    5(t2−10t−25) 5 \left( t ^ { 2 } - 10 t - 25 \right) 5(t2−10t−25)

Question 5

Write in radical form. Assume all variables represent positive real numbers.
- x1/7x^{1 / 7}x1/7

Accepted Answer

A)    x7\sqrt { x ^ { 7 } }x7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    x7\sqrt [ 7 ] { \mathrm { x } }7xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    1x7\frac { 1 } { \sqrt [ 7 ] { x } }7xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​1​ 
D)    x−7x ^ { - 7 }x−7

Question 6

Factor the trinomial, if possible.
- 72x2+42xy+6y272 x ^ { 2 } + 42 x y + 6 y ^ { 2 }72x2+42xy+6y2

Accepted Answer

A)    6(3x−y) (4x−y) 6 ( 3 x - y )  ( 4 x - y ) 6(3x−y) (4x−y)  
B)    (18x+6y) (4x+y) ( 18 x + 6 y )  ( 4 x + y ) (18x+6y) (4x+y)  
C)    (3x+y) (6x+3y) ( 3 x + y )  ( 6 x + 3 y ) (3x+y) (6x+3y)  
D)    6(3x+y) (4x+y) 6 ( 3 x + y )  ( 4 x + y ) 6(3x+y) (4x+y)

Question 7

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x)  to produce x units of plywood is given by C(x)  , what is the
-Suppose the cost per ton,  yyy , to build an oil platform of  xxx  thousand tons is approximated by  y=y =y=   112,500x+225\frac { 112,500 } { x + 225 }x+225112,500​ . What is the cost per ton for  x=10x = 10x=10  ?

Accepted Answer

A)    $50.00\$ 50.00$50.00 
B)    $478.72\$ 478.72$478.72 
C)    $11250.00\$ 11250.00$11250.00 
D)    $11025.00\$ 11025.00$11025.00

Question 8

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
- 11011^0110

Accepted Answer

A)   1
B)   0
C)   11
D)   -1

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
- 2703103\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }310​3270​​

Accepted Answer

A)    3333 \sqrt [ 3 ] { 3 }333c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)   9
C)   3
D)   27

Question 10

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-A formula for calculating the distance, d, one can see from an airplane to the horizon on a clear day is  d=1.22x1/2\mathrm { d } = 1.22 \mathrm { x } ^ { 1 / 2 }d=1.22x1/2  , where x is the altitude of the plane in feet and d is given in miles. How far can one
See in a plane flying at 30,000 feet? Round your answer to the nearest tenth mile, if necessary.

Accepted Answer

A)   191.3 mi
B)   211.3 mi
C)   18,300 mi
D)   1830 mi

Question 11

Factor, using the given factor. Assume all variables represent positive real numbers.
- 14s1/7−8s−2/7;s−2/714 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }14s1/7−8s−2/7;s−2/7

Accepted Answer

A)    s1/7(14s3/7−83/8) s ^ { 1 / 7 } \left( 14 s ^ { 3 / 7 } - 8 ^ { 3 / 8 } \right) s1/7(14s3/7−83/8)  
B)    s−2/7(14 s3/7−8) \mathrm { s } ^ { - 2 / 7 } \left( 14 \mathrm {~s} ^ { 3 / 7 } - 8 \right) s−2/7(14 s3/7−8)  
C)    s−2/7(14s3/7−8s) s ^ { - 2 / 7 } \left( 14 s ^ { 3 / 7 } - 8 s \right) s−2/7(14s3/7−8s)  
D)    s1/3(14−8s3/8) s ^ { 1 / 3 } \left( 14 - 8 s ^ { 3 / 8 } \right) s1/3(14−8s3/8)

Question 12

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
- 1h(1(x+h) 2+2−1x2+2) \frac { 1 } { h } \left( \frac { 1 } { ( x + h )  ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right) h1​((x+h) 2+21​−x2+21​)

Accepted Answer

A)    −2x+h(x+h) 2(x2+2) \frac { - 2 x + h } { ( x + h )  ^ { 2 } \left( x ^ { 2 } + 2 \right)  }(x+h) 2(x2+2) −2x+h​ 
B)    2x+h((x+h) 2+2) (x2+2) \frac { 2 x + h } { \left( ( x + h )  ^ { 2 } + 2 \right)  \left( x ^ { 2 } + 2 \right)  }((x+h) 2+2) (x2+2) 2x+h​ 
C)    2x((x+h) 2+2) \frac { 2 x } { \left( ( x + h )  ^ { 2 } + 2 \right)  }((x+h) 2+2) 2x​ 
D)    −2x−h((x+h) 2+2) (x2+2) \frac { - 2 x - h } { \left( ( x + h )  ^ { 2 } + 2 \right)  \left( x ^ { 2 } + 2 \right)  }((x+h) 2+2) (x2+2) −2x−h​

Question 13

Solve the problem.
- (3x2+2y) (−4x2−7y+z) \left( 3 x ^ { 2 } + 2 y \right)  \left( - 4 x ^ { 2 } - 7 y + z \right) (3x2+2y) (−4x2−7y+z)

Accepted Answer

A)    −12x2−29xy+3x2z−14y2+2z- 12 x ^ { 2 } - 29 x y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 z−12x2−29xy+3x2z−14y2+2z 
B)    −12x4−29x2y−14y4+3x2yz- 12 x ^ { 4 } - 29 x ^ { 2 } y - 14 y ^ { 4 } + 3 x ^ { 2 } y z−12x4−29x2y−14y4+3x2yz 
C)    −12x4−29x2y2−14y2- 12 x ^ { 4 } - 29 x ^ { 2 } y ^ { 2 } - 14 y ^ { 2 }−12x4−29x2y2−14y2 
D)    −12x4−29x2y+3x2z−14y2+2yz- 12 x ^ { 4 } - 29 x ^ { 2 } y + 3 x ^ { 2 } z - 14 y ^ { 2 } + 2 y z−12x4−29x2y+3x2z−14y2+2yz

Question 14

Factor the polynomial by substitution.
- 9z6+6z3−89 z ^ { 6 } + 6 z ^ { 3 } - 89z6+6z3−8

Accepted Answer

A)    (3z3+2) (3z3−4) \left( 3 z ^ { 3 } + 2 \right)  \left( 3 z ^ { 3 } - 4 \right) (3z3+2) (3z3−4)  
B)    (3z3+4) (3z3−2) \left( 3 z ^ { 3 } + 4 \right)  \left( 3 z ^ { 3 } - 2 \right) (3z3+4) (3z3−2)  
C)    (3z3+1) (3z3−8) \left( 3 z ^ { 3 } + 1 \right)  \left( 3 z ^ { 3 } - 8 \right) (3z3+1) (3z3−8)  
D)    9(z3−2) (z3+4) 9 \left( z ^ { 3 } - 2 \right)  \left( z ^ { 3 } + 4 \right) 9(z3−2) (z3+4)

Question 15

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
- 3−634\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }343−6​

Accepted Answer

A)    1610\frac { 1 } { 6^{10} }6101​ 
B)    −310- 3^{10}−310 
C)    1310\frac { 1 } { 3 ^ { 10 } }3101​ 
D)    1324\frac { 1 } { 3 ^ { 24 } }3241​

Question 16

Factor by any method.
- (2x+1) 2−y2( 2 x + 1 )  ^ { 2 } - y ^ { 2 }(2x+1) 2−y2

Accepted Answer

A)    (2x−1+y) (2x−1−y) ( 2 x - 1 + y )  ( 2 x - 1 - y ) (2x−1+y) (2x−1−y)  
B)   prime
C)    (2x+1+y) (2x−1−y) ( 2 x + 1 + y )  ( 2 x - 1 - y ) (2x+1+y) (2x−1−y)  
D)    (2x+1+y) (2x+1−y) ( 2 x + 1 + y )  ( 2 x + 1 - y ) (2x+1+y) (2x+1−y)

Question 17

Factor, using the given factor. Assume all variables represent positive real numbers.
- (q+6) −3/17+(q+6) −1/17+(q+6) 1/17;(q+6) −3/17( q + 6 )  ^ { - 3 / 17 } + ( q + 6 )  ^ { - 1 / 17 } + ( q + 6 )  ^ { 1 / 17 } ; \quad ( q + 6 )  ^ { - 3 / 17 }(q+6) −3/17+(q+6) −1/17+(q+6) 1/17;(q+6) −3/17

Accepted Answer

A)    (q+6) −3/17[1+(q+6) 1/17+(q+6) 3/17]( q + 6 )  ^ { - 3 / 17 } \left[ 1 + ( q + 6 )  ^ { 1 / 17 } + ( q + 6 )  ^ { 3 / 17 } \right](q+6) −3/17[1+(q+6) 1/17+(q+6) 3/17] 
B)    (q+6) −3/17[1+(q+6) −2/17+(q+6) −4/17]( q + 6 )  ^ { - 3 / 17 } \left[ 1 + ( q + 6 )  ^ { - 2 / 17 } + ( q + 6 )  ^ { - 4 / 17 } \right](q+6) −3/17[1+(q+6) −2/17+(q+6) −4/17] 
C)    (q+6) −3/17[1+(q+6) 2/17+(q+6) 4/17]( q + 6 )  ^ { - 3 / 17 } \left[ 1 + ( q + 6 )  ^ { 2 / 17 } + ( q + 6 )  ^ { 4 / 17 } \right](q+6) −3/17[1+(q+6) 2/17+(q+6) 4/17] 
D)    (q+6) −3/17[1+(q+6) 4/17+(q+6) 6/17]( q + 6 )  ^ { - 3 / 17 } \left[ 1 + ( q + 6 )  ^ { 4 / 17 } + ( q + 6 )  ^ { 6 / 17 } \right](q+6) −3/17[1+(q+6) 4/17+(q+6) 6/17]

Question 18

Evaluate the expression.
- −(3649) 1/2- \left( \frac { 36 } { 49 } \right)  ^ { 1 / 2 }−(4936​) 1/2

Accepted Answer

A)   not a real number
B)    −1849- \frac { 18 } { 49 }−4918​ 
C)    76\frac { 7 } { 6 }67​ 
D)    −67- \frac { 6 } { 7 }−76​

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
- (6+4) (6−4) ( \sqrt { 6 } + 4 )  ( \sqrt { 6 } - 4 ) (6​+4) (6​−4)

Accepted Answer

A)    6−246 - 2 \sqrt { 4 }6−24c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    −10- 10−10 
C)   22
D)   2

Question 20

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-A manufacturer's cost is given b  C=500n1/3+1200C = 500 n ^ { 1 / 3 } + 1200C=500n1/3+1200  , where C is the cost in dollars and n is the number of parts produced. Find the cost when 729 parts are produced.

Accepted Answer

A)   $14,700
B)   $56
C)   $5700
D)   $3450

Exam 1: Review of Basic Concepts

Write in radical form. Assume all variables represent positive real numbers. - $x^{1 / 7}$

Correct Answer
verified

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }$

Correct Answer
verified

Solve the problem. - $\left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right)$

Correct Answer
verified

Decide whether the expression has been simplified correctly. - $5 ^ { 0 } x = x$

Correct Answer
verified

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$

Correct Answer
verified

Factor the trinomial, if possible. - $72 x ^ { 2 } + 42 x y + 6 y ^ { 2 }$

Correct Answer
verified

Evaluate the expression. - $- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }$

Correct Answer
verified

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -A manufacturer's cost is given b $C = 500 n ^ { 1 / 3 } + 1200$ , where C is the cost in dollars and n is the number of parts produced. Find the cost when 729 parts are produced.

Correct Answer
verified

Correct Answer
verified

Factor, using the given factor. Assume all variables represent positive real numbers. - $( q + 6 ) ^ { - 3 / 17 } + ( q + 6 ) ^ { - 1 / 17 } + ( q + 6 ) ^ { 1 / 17 } ; \quad ( q + 6 ) ^ { - 3 / 17 }$

Correct Answer
verified

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }$

Correct Answer
verified

Factor by any method. - $( 2 x + 1 ) ^ { 2 } - y ^ { 2 }$

Correct Answer
verified

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }$

Correct Answer
verified

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }$

Correct Answer
verified

Correct Answer
verified

Factor the polynomial by substitution. - $9 z ^ { 6 } + 6 z ^ { 3 } - 8$

Correct Answer
verified

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

Correct Answer
verified

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $11^0$

Correct Answer
verified

Factor, using the given factor. Assume all variables represent positive real numbers. - $14 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }$

Correct Answer
verified

Factor out the greatest common factor. Simplify the factors, if possible. - $5 t ^ { 2 } - 10 t - 25$

Correct Answer
verified

Exam 1: Review of Basic Concepts

Write in radical form. Assume all variables represent positive real numbers. - x1/7x^{1 / 7}x1/7

Correct AnswerverifiedShow Answer

Simplify the expression. Assume all variables represent positive real numbers. - 2703103\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }310​3270​​

Correct AnswerverifiedShow Answer

Solve the problem. - (3x2+2y) (−4x2−7y+z) \left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right) (3x2+2y) (−4x2−7y+z)

Correct AnswerverifiedShow Answer

Decide whether the expression has been simplified correctly. - 50x=x5 ^ { 0 } x = x50x=x

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Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1h(1(x+h) 2+2−1x2+2) \frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right) h1​((x+h) 2+21​−x2+21​)

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Factor the trinomial, if possible. - 72x2+42xy+6y272 x ^ { 2 } + 42 x y + 6 y ^ { 2 }72x2+42xy+6y2

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Evaluate the expression. - −(3649) 1/2- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }−(4936​) 1/2

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Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 3−634\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }343−6​

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Factor by any method. - (2x+1) 2−y2( 2 x + 1 ) ^ { 2 } - y ^ { 2 }(2x+1) 2−y2

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Simplify the expression. Assume all variables represent positive real numbers. - (−7) 66\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }6(−7) 6​

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Simplify the expression. Assume all variables represent positive real numbers. - 483−333+39\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }348​​−333​​+9​3​​

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Factor the polynomial by substitution. - 9z6+6z3−89 z ^ { 6 } + 6 z ^ { 3 } - 89z6+6z3−8

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Simplify the expression. Assume all variables represent positive real numbers. - (6+4) (6−4) ( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 ) (6​+4) (6​−4)

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Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 11011^0110

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Factor, using the given factor. Assume all variables represent positive real numbers. - 14s1/7−8s−2/7;s−2/714 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }14s1/7−8s−2/7;s−2/7

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Factor out the greatest common factor. Simplify the factors, if possible. - 5t2−10t−255 t ^ { 2 } - 10 t - 255t2−10t−25

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Write in radical form. Assume all variables represent positive real numbers. - $x^{1 / 7}$

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Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 270 } } { \sqrt [ 3 ] { 10 } }$

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Solve the problem. - $\left( 3 x ^ { 2 } + 2 y \right) \left( - 4 x ^ { 2 } - 7 y + z \right)$

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Decide whether the expression has been simplified correctly. - $5 ^ { 0 } x = x$

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Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$

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Factor the trinomial, if possible. - $72 x ^ { 2 } + 42 x y + 6 y ^ { 2 }$

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Evaluate the expression. - $- \left( \frac { 36 } { 49 } \right) ^ { 1 / 2 }$

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Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { - 6 } } { 3 ^ { 4 } }$

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Factor by any method. - $( 2 x + 1 ) ^ { 2 } - y ^ { 2 }$

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Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 6 ] { ( - 7 ) ^ { 6 } }$

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Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 48 } } { 3 } - \frac { 3 \sqrt { 3 } } { 3 } + \frac { \sqrt { 3 } } { \sqrt { 9 } }$

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Factor the polynomial by substitution. - $9 z ^ { 6 } + 6 z ^ { 3 } - 8$

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Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

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Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $11^0$

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Factor, using the given factor. Assume all variables represent positive real numbers. - $14 s ^ { 1 / 7 } - 8 s ^ { - 2 / 7 } ; \quad s ^ { - 2 / 7 }$

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Factor out the greatest common factor. Simplify the factors, if possible. - $5 t ^ { 2 } - 10 t - 25$

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