Question 1

Find the root. Assume that all variables represent nonnegative real numbers.
-$\sqrt [ 4 ] { - 16 }$

Accepted Answer

A)  $- 2$ 
B)  2 
C)  4 
D)  not real number 
A)  $- 2$ 
B)  2 
C)  4 
D)  not real number

Question 2

Find the power of i.
-$( - 2 i ) ^ { 5 }$

Accepted Answer

A)  $- 32 \mathrm { i }$ 
B)  32 
C)  $32 \mathrm { i }$ 
D)  $- 32$ 
A)  $- 32 \mathrm { i }$ 
B)  32 
C)  $32 \mathrm { i }$ 
D)  $- 32$

Question 3

Use the properties of exponents to simplify. Write with positive exponents.
-$\frac { 9 ^ { 3 / 4 } } { 9 ^ { 1 / 4 } }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  3 
D)  9 
A)  $\frac { 1 } { 3 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  3 
D)  9

Question 4

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( 7 \sqrt { x } + 3 ) ( \sqrt { 7 x } - 3 )$

Accepted Answer

A)  $7 x \sqrt { 7 } - 42 \sqrt { x } - 9$ 
B)  $7 x \sqrt { 7 } - 21 \sqrt { x } + 3 \sqrt { 7 x } - 9$ 
C)  $7 x - 9$ 
D)  $7 x - 42 \sqrt { x } - 9$ 
A)  $7 x \sqrt { 7 } - 42 \sqrt { x } - 9$ 
B)  $7 x \sqrt { 7 } - 21 \sqrt { x } + 3 \sqrt { 7 x } - 9$ 
C)  $7 x - 9$ 
D)  $7 x - 42 \sqrt { x } - 9$

Question 5

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 11 } } { 6 z }$

Accepted Answer

A)  $\frac { 11 } { 36 z \sqrt { 11 } }$ 
B)  $\frac { 11 } { 6 z \sqrt { 11 } }$ 
C)  $\frac { 1 } { 6 z \sqrt { 11 } }$ 
D)  $\frac { 1 } { 127 }$ 
A)  $\frac { 11 } { 36 z \sqrt { 11 } }$ 
B)  $\frac { 11 } { 6 z \sqrt { 11 } }$ 
C)  $\frac { 1 } { 6 z \sqrt { 11 } }$ 
D)  $\frac { 1 } { 127 }$

Question 6

Perform the indicated operation. Write the result in the form a + bi.
-$$( 7 - 35 i ) ( 5 - i )$$

Accepted Answer

A)  $- 182 \mathrm { i }$ 
B)  $70 + 182 i$ 
C)  $7 \mathrm { i }$ 
D)  $70 - 182 \mathrm { i }$ 
A)  $- 182 \mathrm { i }$ 
B)  $70 + 182 i$ 
C)  $7 \mathrm { i }$ 
D)  $70 - 182 \mathrm { i }$

Question 7

Find the square root. Assume that all variables represent nonnegative real numbers.
-$\sqrt { x ^ { 40 } }$

Accepted Answer

A)  $x ^ { 40 }$ 
B)  $x ^ { 20 }$ 
C)  $x ^ { 80 }$ 
D)  $x ^ { 2 }$ 
A)  $x ^ { 40 }$ 
B)  $x ^ { 20 }$ 
C)  $x ^ { 80 }$ 
D)  $x ^ { 2 }$

Question 8

Use the quotient rule to divide and simplify.
-$$\sqrt { \frac { x ^ { 17 } } { 49 } }$$

Accepted Answer

A)  $\frac { x ^ { 8 } x } { 7 }$ 
B)  $\frac { x ^ { 8 } \sqrt { x } } { 7 }$ 
C)  $\frac { x \sqrt { \times 15 } } { 7 }$ 
D)  $\frac { \sqrt { \mathrm { x } ^ { 17 } } } { 7 }$ 
A)  $\frac { x ^ { 8 } x } { 7 }$ 
B)  $\frac { x ^ { 8 } \sqrt { x } } { 7 }$ 
C)  $\frac { x \sqrt { \times 15 } } { 7 }$ 
D)  $\frac { \sqrt { \mathrm { x } ^ { 17 } } } { 7 }$

Question 9

Solve.
-$$\sqrt { x + 60 } - \sqrt { x + 32 } = 2$$

Accepted Answer

A)  $- 4$ 
B)  4 
C)  5 
D)  $\varnothing$ 
A)  $- 4$ 
B)  4 
C)  5 
D)  $\varnothing$

Question 10

Use rational exponents to write as a single radical expression.
-$\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }$

Accepted Answer

A)  $x ^ { 21 }$ 
B)  $\sqrt [ 9 ] { \mathrm { x } ^ { 7 } }$ 
C)  $\sqrt { x ^ { 7 } }$ 
D)  $\sqrt [ 9 ] { \mathrm { x } ^ { 3 } }$ 
A)  $x ^ { 21 }$ 
B)  $\sqrt [ 9 ] { \mathrm { x } ^ { 7 } }$ 
C)  $\sqrt { x ^ { 7 } }$ 
D)  $\sqrt [ 9 ] { \mathrm { x } ^ { 3 } }$

Question 11

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$\sqrt { 7 } ( \sqrt { 35 } + \sqrt { 7 } )$

Accepted Answer

A)  $7 \sqrt { 5 } + 49$ 
B)  $49 \sqrt { 5 } + 7$ 
C)  $35 + 49$ 
D)  $7 \sqrt { 5 } + 7$ 
A)  $7 \sqrt { 5 } + 49$ 
B)  $49 \sqrt { 5 } + 7$ 
C)  $35 + 49$ 
D)  $7 \sqrt { 5 } + 7$

Question 12

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 3 ] { 81 }$

Accepted Answer

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

Question 13

Solve.
-$$\sqrt { x ^ { 2 } - 11 } + 5 = 0$$

Accepted Answer

A)  $\{ 6 \}$ 
B)  $\{ 7 , - 7 \}$ 
C)  $\{ 6 , - 6 \}$ 
D)  $\varnothing$ 
A)  $\{ 6 \}$ 
B)  $\{ 7 , - 7 \}$ 
C)  $\{ 6 , - 6 \}$ 
D)  $\varnothing$

Question 14

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 2 } { \sqrt [ 3 ] { 7 } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 14 } } { 7 }$ 
B)  $\frac { 2 \sqrt [ 3 ] { 49 } } { 7 }$ 
C)  $\frac { 2 \sqrt { 7 } } { 7 }$ 
D)  $\frac { 2 \sqrt [ 3 ] { 7 } } { 7 }$ 
A)  $\frac { \sqrt [ 3 ] { 14 } } { 7 }$ 
B)  $\frac { 2 \sqrt [ 3 ] { 49 } } { 7 }$ 
C)  $\frac { 2 \sqrt { 7 } } { 7 }$ 
D)  $\frac { 2 \sqrt [ 3 ] { 7 } } { 7 }$

Question 15

Use radical notation to write the expression. Simplify if possible.
-$\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 4 }$

Question 16

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }$

Accepted Answer

A)  $\frac { t + \sqrt { t m } } { t + m }$ 
B)  $\frac { t - t \sqrt { m } } { t - m }$ 
C)  $\frac { t - \sqrt { t m } } { t - m }$ 
D)  $\frac { t + t \sqrt { m } } { t + m }$ 
A)  $\frac { t + \sqrt { t m } } { t + m }$ 
B)  $\frac { t - t \sqrt { m } } { t - m }$ 
C)  $\frac { t - \sqrt { t m } } { t - m }$ 
D)  $\frac { t + t \sqrt { m } } { t + m }$

Question 17

Find the root. Use absolute value bars when necessary.
-$$\sqrt [ 6 ] { ( 15 x y ) ^ { 6 } }$$

Accepted Answer

A)  $15 | x y |$ 
B)  $15 x y$ 
C)  $15 \sqrt [ 6 ] { x y }$ 
D)  $15 \mid x ^ { 6 } y ^ { 6 }$ 
A)  $15 | x y |$ 
B)  $15 x y$ 
C)  $15 \sqrt [ 6 ] { x y }$ 
D)  $15 \mid x ^ { 6 } y ^ { 6 }$

Question 18

Write in terms of i.
-$$\sqrt { - 280 }$$

Accepted Answer

A)  $- 2 i \sqrt { 70 }$ 
B)  $2 \mathrm { i } \sqrt { 70 }$ 
C)  $2 \sqrt { 70 }$ 
D)  $- 2 \sqrt { 70 }$ 
A)  $- 2 i \sqrt { 70 }$ 
B)  $2 \mathrm { i } \sqrt { 70 }$ 
C)  $2 \sqrt { 70 }$ 
D)  $- 2 \sqrt { 70 }$

Question 19

Simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { x ^ { 13 } } } { \sqrt { 64 } }$

Accepted Answer

A)  $\frac { x ^ { 6 } x } { 8 }$ 
B)  $\frac { x \sqrt { x ^ { 11 } } } { 8 }$ 
C)  $\frac { \sqrt { \mathrm { x } ^ { 13 } } } { 8 }$ 
D)  $\frac { x ^ { 6 } \sqrt { x } } { 8 }$ 
A)  $\frac { x ^ { 6 } x } { 8 }$ 
B)  $\frac { x \sqrt { x ^ { 11 } } } { 8 }$ 
C)  $\frac { \sqrt { \mathrm { x } ^ { 13 } } } { 8 }$ 
D)  $\frac { x ^ { 6 } \sqrt { x } } { 8 }$

Question 20

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt { \frac { 3 x } { 2 y } }$

Accepted Answer

A)  $\frac { \sqrt { 6 x y } } { 4 y ^ { 2 } }$ 
B)  $\sqrt { 6 x y }$ 
C)  $\frac { \sqrt { 6 x y } } { 2 y }$ 
D)  $\frac { \sqrt { 6 x y } } { 2 }$ 
A)  $\frac { \sqrt { 6 x y } } { 4 y ^ { 2 } }$ 
B)  $\sqrt { 6 x y }$ 
C)  $\frac { \sqrt { 6 x y } } { 2 y }$ 
D)  $\frac { \sqrt { 6 x y } } { 2 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 4 ] { - 16 }$

Find the power of i. - $( - 2 i ) ^ { 5 }$

Use the properties of exponents to simplify. Write with positive exponents. - $\frac { 9 ^ { 3 / 4 } } { 9 ^ { 1 / 4 } }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 7 \sqrt { x } + 3 ) ( \sqrt { 7 x } - 3 )$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt { 11 } } { 6 z }$

Perform the indicated operation. Write the result in the form a + bi. - $( 7 - 35 i ) ( 5 - i )$

Find the square root. Assume that all variables represent nonnegative real numbers. - $\sqrt { x ^ { 40 } }$

Use the quotient rule to divide and simplify. - $\sqrt { \frac { x ^ { 17 } } { 49 } }$

Solve. - $\sqrt { x + 60 } - \sqrt { x + 32 } = 2$

Use rational exponents to write as a single radical expression. - $\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 7 } ( \sqrt { 35 } + \sqrt { 7 } )$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 3 ] { 81 }$

Solve. - $\sqrt { x ^ { 2 } - 11 } + 5 = 0$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 2 } { \sqrt [ 3 ] { 7 } }$

Use radical notation to write the expression. Simplify if possible. - $\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }$

Find the root. Use absolute value bars when necessary. - $\sqrt [ 6 ] { ( 15 x y ) ^ { 6 } }$

Write in terms of i. - $\sqrt { - 280 }$

Simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { x ^ { 13 } } } { \sqrt { 64 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt { \frac { 3 x } { 2 y } }$

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Exam 7: Rational Exponents, Radicals, and Complex Numbers

Find the root. Assume that all variables represent nonnegative real numbers. - −164\sqrt [ 4 ] { - 16 }4−16​

Find the power of i. - (−2i)5( - 2 i ) ^ { 5 }(−2i)5

Use the properties of exponents to simplify. Write with positive exponents. - 93/491/4\frac { 9 ^ { 3 / 4 } } { 9 ^ { 1 / 4 } }91/493/4​

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (7x+3)(7x−3)( 7 \sqrt { x } + 3 ) ( \sqrt { 7 x } - 3 )(7x​+3)(7x​−3)

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 116z\frac { \sqrt { 11 } } { 6 z }6z11​​

Perform the indicated operation. Write the result in the form a + bi. - (7−35i)(5−i)( 7 - 35 i ) ( 5 - i )(7−35i)(5−i)

Find the square root. Assume that all variables represent nonnegative real numbers. - x40\sqrt { x ^ { 40 } }x40​

Use the quotient rule to divide and simplify. - x1749\sqrt { \frac { x ^ { 17 } } { 49 } }49x17​​

Solve. - x+60−x+32=2\sqrt { x + 60 } - \sqrt { x + 32 } = 2x+60​−x+32​=2

Use rational exponents to write as a single radical expression. - x9⋅x23\sqrt [ 9 ] { x } \cdot \sqrt [ 3 ] { x ^ { 2 } }9x​⋅3x2​

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - 7(35+7)\sqrt { 7 } ( \sqrt { 35 } + \sqrt { 7 } )7​(35​+7​)

Simplify. Assume that all variables represent positive real numbers. - 813\sqrt [ 3 ] { 81 }381​

Solve. - x2−11+5=0\sqrt { x ^ { 2 } - 11 } + 5 = 0x2−11​+5=0

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 273\frac { 2 } { \sqrt [ 3 ] { 7 } }37​2​

Use radical notation to write the expression. Simplify if possible. - (864)2/3\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }(648​)2/3

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - tt+m\frac { \sqrt { t } } { \sqrt { t } + \sqrt { m } }t​+m​t​​

Find the root. Use absolute value bars when necessary. - (15xy)66\sqrt [ 6 ] { ( 15 x y ) ^ { 6 } }6(15xy)6​

Write in terms of i. - −280\sqrt { - 280 }−280​

Simplify. Assume that all variables represent positive real numbers. - x1364\frac { \sqrt { x ^ { 13 } } } { \sqrt { 64 } }64​x13​​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 3x2y\sqrt { \frac { 3 x } { 2 y } }2y3x​​