Question 1

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { 4 }$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  not a real number 
C)  16 
D)  2 
A)  $\frac { 1 } { 4 }$ 
B)  not a real number 
C)  16 
D)  2

Question 2

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { - 64 }$

Accepted Answer

A)  4096 
B)  $\frac { 8 } { 64 }$ 
C)  8 
D)  not a real number 
A)  4096 
B)  $\frac { 8 } { 64 }$ 
C)  8 
D)  not a real number

Question 3

Rewrite the expression with a rational exponent.
-$\sqrt { x ^ { 5 } }$

Accepted Answer

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

Question 4

Rewrite the expression with a rational exponent.
-$\sqrt [ 3 ] { 5 p }$

Accepted Answer

A)  $( 5 p ) ^ { 3 }$ 
B)  $\frac { 1 } { ( 5 p ) ^ { 3 } }$ 
C)  $5 ^ { 1 / 3 } \mathrm { p }$ 
D)  $( 5 p ) ^ { 1 / 3 }$ 
A)  $( 5 p ) ^ { 3 }$ 
B)  $\frac { 1 } { ( 5 p ) ^ { 3 } }$ 
C)  $5 ^ { 1 / 3 } \mathrm { p }$ 
D)  $( 5 p ) ^ { 1 / 3 }$

Question 5

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }$

Accepted Answer

A)  $- 4$ 
B)  $| - 256 |$ 
C)  $- | - 4 |$ 
D)  4 
A)  $- 4$ 
B)  $| - 256 |$ 
C)  $- | - 4 |$ 
D)  4

Question 6

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-(b7)2/7

Accepted Answer

A)  b2 
B)  b1/2 
C)  b2/9 
D)  b9/7 
A)  b2 
B)  b1/2 
C)  b2/9 
D)  b9/7

Question 7

Use radical notation to rewrite the expression. Simplify, if possible.
-$144 ^ { 1 / 2 }$

Accepted Answer

A)  72 
B)  12 
C)  6 
D)  $\frac { 1 } { 6 }$ 
A)  72 
B)  12 
C)  6 
D)  $\frac { 1 } { 6 }$

Question 8

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$\frac { \left( 3 x ^ { 5 / 7 } \right) ^ { 4 } } { x ^ { 1 / 7 } }$

Accepted Answer

A)  $81 x ^ { 19 / 7 }$ 
B)  $27 x ^ { 8 / 7 }$ 
C)  $3 x ^ { 19 / 7 }$ 
D)  $81 x ^ { 5 }$ 
A)  $81 x ^ { 19 / 7 }$ 
B)  $27 x ^ { 8 / 7 }$ 
C)  $3 x ^ { 19 / 7 }$ 
D)  $81 x ^ { 5 }$

Question 9

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

Accepted Answer

A)  $\sqrt { 10 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  25 
D)  5 
A)  $\sqrt { 10 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  25 
D)  5

Question 10

Find the square root if it is a real number, or state that the expression is not a real number.
-- 0.49

Accepted Answer

A)  not a real number 
B)  0.07 
C)  -0.7 
D)  -0.07 
A)  not a real number 
B)  0.07 
C)  -0.7 
D)  -0.07

Question 11

Find the indicated root, or state that the expression is not a real number.
-$\sqrt [ 5 ] { - 1 }$

Accepted Answer

A)  $- \frac { 1 } { 5 }$ 
B)  not a real number 
C)  1 
D)  $- 1$ 
A)  $- \frac { 1 } { 5 }$ 
B)  not a real number 
C)  1 
D)  $- 1$

Question 12

Use radical notation to rewrite the expression. Simplify, if possible.
-$( - 64 ) ^ { 4 / 3 }$

Accepted Answer

A)  not a real number 
B)  256 
C)  4096 
D)  $- 256$ 
A)  not a real number 
B)  256 
C)  4096 
D)  $- 256$

Question 13

Rewrite the expression with a positive rational exponent. Simplify, if possible.
-$9 ^ { - 1 / 2 }$

Accepted Answer

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

Question 14

Use radical notation to rewrite the expression. Simplify, if possible.
-$625 ^ { 5 / 4 }$

Accepted Answer

A)  390,625 
B)  78,125 
C)  3125 
D)  $1,953,125$ 
A)  390,625 
B)  78,125 
C)  3125 
D)  $1,953,125$

Question 15

Find the indicated function value for the function.
-Evaluate $g ( x ) = - \sqrt [ 3 ] { - 2 x - 70 }$ for $g ( - 3 )$

Accepted Answer

A)  not a real number 
B)  $- 4$ 
C)  $\sqrt [ 3 ] { 4 }$ 
D)  4 
A)  not a real number 
B)  $- 4$ 
C)  $\sqrt [ 3 ] { 4 }$ 
D)  4

Question 16

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so.
-$$\text { Evaluate } t ( x ) = - \sqrt { x + 6 } \text { for } t ( - 2 )$$

Accepted Answer

A)  -1.41 
B)  2 
C)  -2 
D)  not a real number 
A)  -1.41 
B)  2 
C)  -2 
D)  not a real number

Question 17

Rewrite the expression with a rational exponent.
-$\sqrt [ 3 ] { x ^ { 5 } }$

Accepted Answer

A)  $x ^ { 3 / 5 }$ 
B)  $\frac { x ^ { 5 } } { 3 }$ 
C)  $x ^ { 2 }$ 
D)  $x ^ { 5 / 3 }$ 
A)  $x ^ { 3 / 5 }$ 
B)  $\frac { x ^ { 5 } } { 3 }$ 
C)  $x ^ { 2 }$ 
D)  $x ^ { 5 / 3 }$

Question 18

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { 30 - 5 }$

Accepted Answer

A)  25 
B)  $\sqrt { 30 } + \sqrt { 5 }$ 
C)  5 
D)  not a real number 
A)  25 
B)  $\sqrt { 30 } + \sqrt { 5 }$ 
C)  5 
D)  not a real number

Question 19

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so.
-$$\text { Evaluate } f ( x ) = - \sqrt { 2 x + 5 } \text { for } f ( 2 )$$

Accepted Answer

A)  -1.73 
B)  3 
C)  not a real number 
D)  -3 
A)  -1.73 
B)  3 
C)  not a real number 
D)  -3

Question 20

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$$\left( x ^ { - 1 / 4 } y ^ { 7 / 5 } \right) ^ { 3 / 4 }$$

Accepted Answer

A)  $x ^ { 1 / 2 } y ^ { 43 / 12 }$ 
B)  $x ^ { 3 / 16 } y ^ { 21 / 20 }$ 
C)  $\frac { y ^ { 21 / 20 } } { 3 / 16 }$ 
D)  $- x ^ { 3 / 16 } y ^ { 21 / 20 }$ 
A)  $x ^ { 1 / 2 } y ^ { 43 / 12 }$ 
B)  $x ^ { 3 / 16 } y ^ { 21 / 20 }$ 
C)  $\frac { y ^ { 21 / 20 } } { 3 / 16 }$ 
D)  $- x ^ { 3 / 16 } y ^ { 21 / 20 }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { 4 }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { - 64 }$

Rewrite the expression with a rational exponent. - $\sqrt { x ^ { 5 } }$

Rewrite the expression with a rational exponent. - $\sqrt [ 3 ] { 5 p }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -(b⁷)^2/7

Use radical notation to rewrite the expression. Simplify, if possible. - $144 ^ { 1 / 2 }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\frac { \left( 3 x ^ { 5 / 7 } \right) ^ { 4 } } { x ^ { 1 / 7 } }$

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

Find the square root if it is a real number, or state that the expression is not a real number. -- 0.49

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 5 ] { - 1 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $( - 64 ) ^ { 4 / 3 }$

Rewrite the expression with a positive rational exponent. Simplify, if possible. - $9 ^ { - 1 / 2 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $625 ^ { 5 / 4 }$

Find the indicated function value for the function. -Evaluate $g ( x ) = - \sqrt [ 3 ] { - 2 x - 70 }$ for $g ( - 3 )$

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so. - $\text { Evaluate } t ( x ) = - \sqrt { x + 6 } \text { for } t ( - 2 )$

Rewrite the expression with a rational exponent. - $\sqrt [ 3 ] { x ^ { 5 } }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { 30 - 5 }$

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so. - $\text { Evaluate } f ( x ) = - \sqrt { 2 x + 5 } \text { for } f ( 2 )$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\left( x ^ { - 1 / 4 } y ^ { 7 / 5 } \right) ^ { 3 / 4 }$

Algebra, Mathematical Models, and Problem Solving

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Exam 7: Radicals, Radical Functions, and Rational Exponents

Find the square root if it is a real number, or state that the expression is not a real number. - 4\sqrt { 4 }4​

Find the square root if it is a real number, or state that the expression is not a real number. - −64\sqrt { - 64 }−64​

Rewrite the expression with a rational exponent. - x5\sqrt { x ^ { 5 } }x5​

Rewrite the expression with a rational exponent. - 5p3\sqrt [ 3 ] { 5 p }35p​

Simplify the expression. Include absolute value bars where necessary. - (−4)44\sqrt [ 4 ] { ( - 4 ) ^ { 4 } }4(−4)4​

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. -(b7)2/7

Use radical notation to rewrite the expression. Simplify, if possible. - 1441/2144 ^ { 1 / 2 }1441/2

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - (3x5/7)4x1/7\frac { \left( 3 x ^ { 5 / 7 } \right) ^ { 4 } } { x ^ { 1 / 7 } }x1/7(3x5/7)4​

Simplify the expression. - 52\sqrt { 5 ^ { 2 } }52​