Question 1

Simplify the expression.
-$\sqrt { 4 x ^ { 8 } }$

Accepted Answer

A)  $2 x ^ { 8 }$ 
B)  $4 x ^ { 4 }$ 
C)  $| 2 x |$ 
D)  $2 x ^ { 4 }$ 
A)  $2 x ^ { 8 }$ 
B)  $4 x ^ { 4 }$ 
C)  $| 2 x |$ 
D)  $2 x ^ { 4 }$

Question 2

Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
-$$f ( x ) = \sqrt { x - 2 }$$

Accepted Answer

A)  domain of $\mathrm { f: } [ 2 , \infty )$
  
B)  domain of $f : [ - 2 , \infty )$
  
C)  domain of $f : ( - , - 2 ]$
  
D)  domain of $f : ( * , 2 ]$
  
A)  domain of $\mathrm { f: } [ 2 , \infty )$
  
B)  domain of $f : [ - 2 , \infty )$
  
C)  domain of $f : ( - , - 2 ]$
  
D)  domain of $f : ( * , 2 ]$

Question 3

Solve the problem.
-The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 25 months of age and a child 16 months of age?

Accepted Answer

A)  43.1 in. 
B)  14.5 in. 
C)  4.9 in. 
D)  2.9 in. 
A)  43.1 in. 
B)  14.5 in. 
C)  4.9 in. 
D)  2.9 in.

Question 4

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-z-2/7 ·z3/7

Accepted Answer

A)  z6/7 
B)  z7/6 
C)  z1/7 
D)  z-1/7 
A)  z6/7 
B)  z7/6 
C)  z1/7 
D)  z-1/7

Question 5

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$\frac { x ^ { 4 / 3 } x ^ { - 3 / 4 } } { x ^ { 2 / 7 } }$

Accepted Answer

A)  $x ^ { 73 / 84 }$ 
B)  $\frac { 1 } { x ^ { 25 / 84 } }$ 
C)  $\frac { 1 } { x ^ { 73 / 84 } }$ 
D)  $x ^ { 25 / 84 }$ 
A)  $x ^ { 73 / 84 }$ 
B)  $\frac { 1 } { x ^ { 25 / 84 } }$ 
C)  $\frac { 1 } { x ^ { 73 / 84 } }$ 
D)  $x ^ { 25 / 84 }$

Question 6

Use radical notation to rewrite the expression. Simplify, if possible.
-$( 125 ) ^ { 2 / 3 }$

Accepted Answer

A)  5 
B)  $\frac { 250 } { 3 }$ 
C)  10 
D)  25 
A)  5 
B)  $\frac { 250 } { 3 }$ 
C)  10 
D)  25

Question 7

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 5 ] { ( - 2 ) ^ { 5 } }$

Accepted Answer

A)  $- 2$ 
B)  $| - 2 |$ 
C)  2 
D)  $( - 2 ) ^ { 5 }$ 
A)  $- 2$ 
B)  $| - 2 |$ 
C)  2 
D)  $( - 2 ) ^ { 5 }$

Question 8

Find the cube root.
-$$\sqrt [ 3 ] { 125 }$$

Accepted Answer

A)  11 
B)  5 
C)  25 
D)  ±5 
A)  11 
B)  5 
C)  25 
D)  ±5

Question 9

Use radical notation to rewrite the expression. Simplify, if possible.
-$( - 27 ) ^ { 1 / 3 }$

Accepted Answer

A)  $- 3 \sqrt [ 3 ] { 9 }$ 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$ 
A)  $- 3 \sqrt [ 3 ] { 9 }$ 
B)  3 
C)  $- 3$ 
D)  $- \frac { 1 } { 3 }$

Question 10

Find the indicated function value for the function.
-Evaluate $m ( x ) = - \sqrt [ 3 ] { 2 x - 2 }$ for $m ( 5 )$

Accepted Answer

A)  $\sqrt [ 3 ] { 2 }$ 
B)  2 
C)  3 
D)  $- 2$ 
A)  $\sqrt [ 3 ] { 2 }$ 
B)  2 
C)  3 
D)  $- 2$

Question 11

Find the indicated root, or state that the expression is not a real number.
-$\sqrt [ 3 ] { 64 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 4 }$ 
B)  12 
C)  4 
D)  $- 4$ 
A)  $\sqrt [ 3 ] { 4 }$ 
B)  12 
C)  4 
D)  $- 4$

Question 12

Rewrite the expression with a rational exponent.
-$$2 y \sqrt [ 4 ] { x ^ { 5 } }$$

Accepted Answer

A)  $2 y x ^ { 4 / 5 }$ 
B)  $2 y x ^ { 5 / 4 }$ 
C)  $( 2 y x ) ^ { 5 / 4 }$ 
D)  $\frac { 2 y x ^ { 5 } } { 4 }$ 
A)  $2 y x ^ { 4 / 5 }$ 
B)  $2 y x ^ { 5 / 4 }$ 
C)  $( 2 y x ) ^ { 5 / 4 }$ 
D)  $\frac { 2 y x ^ { 5 } } { 4 }$

Question 13

Use radical notation to rewrite the expression. Simplify, if possible.
-$125 ^ { 4 / 3 }$

Accepted Answer

A)  78,125 
B)  3125 
C)  15,625 
D)  625 
A)  78,125 
B)  3125 
C)  15,625 
D)  625

Question 14

Rewrite the expression with a rational exponent.
-$\left( \sqrt [ 7 ] { 2 x ^ { 2 } y } \right) ^ { 8 }$

Accepted Answer

A)  $\frac { \left( 2 x ^ { 2 } y \right) ^ { 7 } } { 8 }$ 
B)  $\left( 2 x ^ { 2 } y \right) ^ { 8 / 7 }$ 
C)  $\left( 2 x ^ { 2 } y \right) ^ { 7 / 8 }$ 
D)  $\frac { \left( 2 x ^ { 2 } y \right) ^ { 8 } } { 7 }$ 
A)  $\frac { \left( 2 x ^ { 2 } y \right) ^ { 7 } } { 8 }$ 
B)  $\left( 2 x ^ { 2 } y \right) ^ { 8 / 7 }$ 
C)  $\left( 2 x ^ { 2 } y \right) ^ { 7 / 8 }$ 
D)  $\frac { \left( 2 x ^ { 2 } y \right) ^ { 8 } } { 7 }$

Question 15

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-(r1/9 s1/9)2

Accepted Answer

A)  r1/18 s1/18 
B)  r2s2 
C)  r2/9 s2/9 
D)  r1/81 s1/81 
A)  r1/18 s1/18 
B)  r2s2 
C)  r2/9 s2/9 
D)  r1/81 s1/81

Question 16

Use radical notation to rewrite the expression. Simplify, if possible.
-$32 ^ { 4 / 5 }$

Accepted Answer

A)  512 
B)  16 
C)  128 
D)  256 
A)  512 
B)  16 
C)  128 
D)  256

Question 17

Simplify the expression.
-$$\sqrt { ( x - 5 ) ^ { 2 } }$$

Accepted Answer

A)  $| x - 5 |$ 
B)  $- 5 \sqrt { x }$ 
C)  $x - 5$ 
D)  $x ^ { 2 } - 10 x + 25$ 
A)  $| x - 5 |$ 
B)  $- 5 \sqrt { x }$ 
C)  $x - 5$ 
D)  $x ^ { 2 } - 10 x + 25$

Question 18

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { \frac { 49 } { 256 } }$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 7 } { 17 }$ 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 7 } { 16 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 7 } { 17 }$ 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 7 } { 16 }$

Question 19

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$\left( y ^ { - 7 / 8 } \right) ^ { - 1 / 3 }$

Accepted Answer

A)  $\frac { 1 } { y ^ { 29 / 24 } }$ 
B)  $y ^ { 7 / 24 }$ 
C)  $\frac { 1 } { y ^ { 7 / 24 } }$ 
D)  $\mathrm { y } ^ { 29 / 24 }$ 
A)  $\frac { 1 } { y ^ { 29 / 24 } }$ 
B)  $y ^ { 7 / 24 }$ 
C)  $\frac { 1 } { y ^ { 7 / 24 } }$ 
D)  $\mathrm { y } ^ { 29 / 24 }$

Question 20

Rewrite the expression with a rational exponent.
-$( \sqrt { 23 x y } ) ^ { 7 }$

Accepted Answer

A)  $( 23 x y ) ^ { 7 / 2 }$ 
B)  $\frac { ( 23 x y ) ^ { 2 } } { 7 }$ 
C)  $\frac { ( 23 x y ) ^ { 7 } } { 2 }$ 
D)  $( 23 x y ) ^ { 2 / 7 }$ 
A)  $( 23 x y ) ^ { 7 / 2 }$ 
B)  $\frac { ( 23 x y ) ^ { 2 } } { 7 }$ 
C)  $\frac { ( 23 x y ) ^ { 7 } } { 2 }$ 
D)  $( 23 x y ) ^ { 2 / 7 }$

Simplify the expression. - $\sqrt { 4 x ^ { 8 } }$

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - $f ( x ) = \sqrt { x - 2 }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -z^-2/7 ·z^3/7

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\frac { x ^ { 4 / 3 } x ^ { - 3 / 4 } } { x ^ { 2 / 7 } }$

Use radical notation to rewrite the expression. Simplify, if possible. - $( 125 ) ^ { 2 / 3 }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 5 ] { ( - 2 ) ^ { 5 } }$

Find the cube root. - $\sqrt [ 3 ] { 125 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $( - 27 ) ^ { 1 / 3 }$

Find the indicated function value for the function. -Evaluate $m ( x ) = - \sqrt [ 3 ] { 2 x - 2 }$ for $m ( 5 )$

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 3 ] { 64 }$

Rewrite the expression with a rational exponent. - $2 y \sqrt [ 4 ] { x ^ { 5 } }$

Use radical notation to rewrite the expression. Simplify, if possible. - $125 ^ { 4 / 3 }$

Rewrite the expression with a rational exponent. - $\left( \sqrt [ 7 ] { 2 x ^ { 2 } y } \right) ^ { 8 }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -(r^1/9 s^1/9)²

Use radical notation to rewrite the expression. Simplify, if possible. - $32 ^ { 4 / 5 }$

Simplify the expression. - $\sqrt { ( x - 5 ) ^ { 2 } }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { \frac { 49 } { 256 } }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\left( y ^ { - 7 / 8 } \right) ^ { - 1 / 3 }$

Rewrite the expression with a rational exponent. - $( \sqrt { 23 x y } ) ^ { 7 }$

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Exam 7: Radicals, Radical Functions, and Rational Exponents

Simplify the expression. - 4x8\sqrt { 4 x ^ { 8 } }4x8​

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - f(x)=x−2f ( x ) = \sqrt { x - 2 }f(x)=x−2​

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -z-2/7 ·z3/7

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - x4/3x−3/4x2/7\frac { x ^ { 4 / 3 } x ^ { - 3 / 4 } } { x ^ { 2 / 7 } }x2/7x4/3x−3/4​

Use radical notation to rewrite the expression. Simplify, if possible. - (125)2/3( 125 ) ^ { 2 / 3 }(125)2/3

Simplify the expression. Include absolute value bars where necessary. - (−2)55\sqrt [ 5 ] { ( - 2 ) ^ { 5 } }5(−2)5​

Find the cube root. - 1253\sqrt [ 3 ] { 125 }3125​

Use radical notation to rewrite the expression. Simplify, if possible. - (−27)1/3( - 27 ) ^ { 1 / 3 }(−27)1/3

Find the indicated function value for the function. -Evaluate m(x)=−2x−23m ( x ) = - \sqrt [ 3 ] { 2 x - 2 }m(x)=−32x−2​ for m(5)m ( 5 )m(5)

Find the indicated root, or state that the expression is not a real number. - 643\sqrt [ 3 ] { 64 }364​

Rewrite the expression with a rational exponent. - 2yx542 y \sqrt [ 4 ] { x ^ { 5 } }2y4x5​

Use radical notation to rewrite the expression. Simplify, if possible. - 1254/3125 ^ { 4 / 3 }1254/3

Rewrite the expression with a rational exponent. - (2x2y7)8\left( \sqrt [ 7 ] { 2 x ^ { 2 } y } \right) ^ { 8 }(72x2y​)8

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -(r1/9 s1/9)2

Use radical notation to rewrite the expression. Simplify, if possible. - 324/532 ^ { 4 / 5 }324/5

Simplify the expression. - (x−5)2\sqrt { ( x - 5 ) ^ { 2 } }(x−5)2​

Find the square root if it is a real number, or state that the expression is not a real number. - 49256\sqrt { \frac { 49 } { 256 } }25649​​

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - (y−7/8)−1/3\left( y ^ { - 7 / 8 } \right) ^ { - 1 / 3 }(y−7/8)−1/3

Rewrite the expression with a rational exponent. - (23xy)7( \sqrt { 23 x y } ) ^ { 7 }(23xy​)7