Question 1

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  11 
B)  15 
C)  14 
D)  12 
A)  11 
B)  15 
C)  14 
D)  12

Question 2

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

Accepted Answer

A)  $25 - 49 \mathrm { i }$ 
B)  $- 24 + 0 \mathrm { i }$ 
C)  $25 - 49 i ^ { 2 }$ 
D)  $74 + 0 \mathrm { i }$ 
A)  $25 - 49 \mathrm { i }$ 
B)  $- 24 + 0 \mathrm { i }$ 
C)  $25 - 49 i ^ { 2 }$ 
D)  $74 + 0 \mathrm { i }$

Question 3

Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 3 + 3 i } { 7 - 3 i }$

Accepted Answer

A)  $\frac { 30 } { 29 } - \frac { 12 } { 29 } \mathrm { i }$ 
B)  $\frac { 3 } { 20 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 3 } { 4 } - \frac { 3 } { 8 } \mathrm { i }$ 
D)  $\frac { 6 } { 29 } + \frac { 15 } { 29 } \mathrm { i }$ 
A)  $\frac { 30 } { 29 } - \frac { 12 } { 29 } \mathrm { i }$ 
B)  $\frac { 3 } { 20 } - \frac { 3 } { 8 } \mathrm { i }$ 
C)  $\frac { 3 } { 4 } - \frac { 3 } { 8 } \mathrm { i }$ 
D)  $\frac { 6 } { 29 } + \frac { 15 } { 29 } \mathrm { i }$

Question 4

Write with positive exponents. Simplify if possible.
-$64 ^ { - 4 / 3 }$

Accepted Answer

A)  $\frac { 1 } { 256 }$ 
B)  not a real number 
C)  $- \frac { 1 } { 256 }$ 
D)  256 
A)  $\frac { 1 } { 256 }$ 
B)  not a real number 
C)  $- \frac { 1 } { 256 }$ 
D)  256

Question 5

Rationalize the denominator. Assume that all variables represent positive numbers.
-$\frac { \sqrt [ 3 ] { 5 x } } { \sqrt [ 3 ] { 6 y } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 180 x y } } { 6 y }$ 
B)  $\frac { \sqrt [ 3 ] { 1080 x y ^ { 2 } } } { 6 y }$ 
C)  $\frac { \sqrt [ 3 ] { 180 x y ^ { 2 } } } { 6 y }$ 
D)  $\frac { 180 x } { 6 y }$ 
A)  $\frac { \sqrt [ 3 ] { 180 x y } } { 6 y }$ 
B)  $\frac { \sqrt [ 3 ] { 1080 x y ^ { 2 } } } { 6 y }$ 
C)  $\frac { \sqrt [ 3 ] { 180 x y ^ { 2 } } } { 6 y }$ 
D)  $\frac { 180 x } { 6 y }$

Question 6

Find the square root. Assume that all variables represent positive real numbers.
-$\sqrt { 81 x ^ { 8 } }$

Accepted Answer

A)  $9 x ^ { 2 }$ 
B)  $9 x ^ { 4 }$ 
C)  $9 x ^ { 8 }$ 
D)  $81 x ^ { 4 }$ 
A)  $9 x ^ { 2 }$ 
B)  $9 x ^ { 4 }$ 
C)  $9 x ^ { 8 }$ 
D)  $81 x ^ { 4 }$

Question 7

Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\left( b ^ { 7 } \right) ^ { 2 / 7 }$

Accepted Answer

A)  $b ^ { 2 }$ 
B)  $b ^ { 9 / 7 }$ 
C)  $b ^ { 1 / 2 }$ 
D)  $b ^ { 2 / 49 }$ 
A)  $b ^ { 2 }$ 
B)  $b ^ { 9 / 7 }$ 
C)  $b ^ { 1 / 2 }$ 
D)  $b ^ { 2 / 49 }$

Question 8

Use radical notation to write the expression. Simplify if possible.
-$\left( \frac { 1 } { 16 } \right) ^ { 1 / 2 }$

Accepted Answer

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

Question 9

Use rational exponents to simplify the following.
-$\sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 6 } }$

Accepted Answer

A)  $y ^ { 3 / 3 } z ^ { 3 / 2 }$ 
B)  $y ^ { 2 / 3 }$ 
C)  $y ^ { 2 / 3 } z$ 
D)  $\mathrm { y } ^ { 3 / 2 } \mathrm { z }$ 
A)  $y ^ { 3 / 3 } z ^ { 3 / 2 }$ 
B)  $y ^ { 2 / 3 }$ 
C)  $y ^ { 2 / 3 } z$ 
D)  $\mathrm { y } ^ { 3 / 2 } \mathrm { z }$

Question 10

Use a calculator to approximate the number to three decimal places.
-$\sqrt { 356 }$

Accepted Answer

A)  $18.868$ 
B)  $356.000$ 
C)  $18.865$ 
D)  $18.873$ 
A)  $18.868$ 
B)  $356.000$ 
C)  $18.865$ 
D)  $18.873$

Question 11

Perform the indicated operation. Write the result in the form a + bi.
-$2 \mathrm { i } ( 2 - 8 \mathrm { i } )$

Accepted Answer

A)  $- 16 + 4 \mathrm { i }$ 
B)  $4 \mathrm { i } + 16 \mathrm { i } 2$ 
C)  $4 \mathrm { i } - 16 \mathrm { i } ^ { 2 }$ 
D)  $16 + 4 \mathrm { i }$ 
A)  $- 16 + 4 \mathrm { i }$ 
B)  $4 \mathrm { i } + 16 \mathrm { i } 2$ 
C)  $4 \mathrm { i } - 16 \mathrm { i } ^ { 2 }$ 
D)  $16 + 4 \mathrm { i }$

Question 12

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive
exponents.
-$\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

Accepted Answer

A)  $4 y ^ { 5 }$ 
B)  $4 y ^ { 5 / 3 }$ 
C)  $4 y ^ { 3 / 5 }$ 
D)  $y ^ { 5 / 3 }$ 
A)  $4 y ^ { 5 }$ 
B)  $4 y ^ { 5 / 3 }$ 
C)  $4 y ^ { 3 / 5 }$ 
D)  $y ^ { 5 / 3 }$

Question 13

Write the conjugate of the expression.
-$3 - \sqrt { b }$

Accepted Answer

A)  $- 3 - \sqrt { b }$ 
B)  $3 + \sqrt { b }$ 
C)  $\sqrt { \mathrm { b } }$ 
D)  $\sqrt { \mathrm { b } } - 3$ 
A)  $- 3 - \sqrt { b }$ 
B)  $3 + \sqrt { b }$ 
C)  $\sqrt { \mathrm { b } }$ 
D)  $\sqrt { \mathrm { b } } - 3$

Question 14

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive
exponents.
-$\left( \frac { 64 x ^ { 3 } } { 216 } \right) ^ { 4 / 3 }$

Accepted Answer

A)  $\frac { 256 x ^ { 4 } } { 1296 }$ 
B)  $\frac { 64 x ^ { 4 } } { 216 }$ 
C)  $\frac { 64 x ^ { 13 / 3 } } { 216 }$ 
D)  $\frac { 4 x } { 6 }$ 
A)  $\frac { 256 x ^ { 4 } } { 1296 }$ 
B)  $\frac { 64 x ^ { 4 } } { 216 }$ 
C)  $\frac { 64 x ^ { 13 / 3 } } { 216 }$ 
D)  $\frac { 4 x } { 6 }$

Question 15

Find the root. Assume that all variables represent nonnegative real numbers.
-$- \sqrt [ 4 ] { 1296 }$

Accepted Answer

A)  $- 6$ 
B)  not a real number 
C)  $10.645$ 
D)  36 
A)  $- 6$ 
B)  not a real number 
C)  $10.645$ 
D)  36

Question 16

Find the distance between the pair of points.
-$( - 7 , - 2 )$ and $( 3 , - 6 )$

Accepted Answer

A)  14 units 
B)  84 units 
C)  $84 \sqrt { 21 }$ units 
D)  $2 \sqrt { 29 }$ units 
A)  14 units 
B)  84 units 
C)  $84 \sqrt { 21 }$ units 
D)  $2 \sqrt { 29 }$ units

Question 17

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive
exponents.
-$\sqrt { 529 }$

Accepted Answer

A)  not a real number 
B)  264 
C)  23 
D)  24 
A)  not a real number 
B)  264 
C)  23 
D)  24

Question 18

Find the distance between the pair of points.
-$( 2,3 )$ and $( - 7 , - 5 )$

Accepted Answer

A)  $\sqrt { 145 }$ units 
B)  145 units 
C)  72 units 
D)  $\sqrt { 17 }$ units 
A)  $\sqrt { 145 }$ units 
B)  145 units 
C)  72 units 
D)  $\sqrt { 17 }$ units

Question 19

Use the Pythagorean theorem to find the unknown side of the right triangle.
-

Accepted Answer

A)  145 
B)  $\sqrt { 145 }$ 
C)  $\sqrt { 17 }$ 
D)  17 
A)  145 
B)  $\sqrt { 145 }$ 
C)  $\sqrt { 17 }$ 
D)  17

Question 20

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( 8 \sqrt { 3 } - 3 ) ^ { 2 }$

Accepted Answer

A)  $183 - 48 \sqrt { 3 }$ 
B)  $189 - 48 \sqrt { 3 }$ 
C)  $201 + 48 \sqrt { 3 }$ 
D)  $201 - 48 \sqrt { 3 }$ 
A)  $183 - 48 \sqrt { 3 }$ 
B)  $189 - 48 \sqrt { 3 }$ 
C)  $201 + 48 \sqrt { 3 }$ 
D)  $201 - 48 \sqrt { 3 }$

Use the Pythagorean theorem to find the unknown side of the right triangle. -

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

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 3 + 3 i } { 7 - 3 i }$

Write with positive exponents. Simplify if possible. - $64 ^ { - 4 / 3 }$

Rationalize the denominator. Assume that all variables represent positive numbers. - $\frac { \sqrt [ 3 ] { 5 x } } { \sqrt [ 3 ] { 6 y } }$

Find the square root. Assume that all variables represent positive real numbers. - $\sqrt { 81 x ^ { 8 } }$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\left( b ^ { 7 } \right) ^ { 2 / 7 }$

Use radical notation to write the expression. Simplify if possible. - $\left( \frac { 1 } { 16 } \right) ^ { 1 / 2 }$

Use rational exponents to simplify the following. - $\sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 6 } }$

Use a calculator to approximate the number to three decimal places. - $\sqrt { 356 }$

Perform the indicated operation. Write the result in the form a + bi. - $2 \mathrm { i } ( 2 - 8 \mathrm { i } )$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

Write the conjugate of the expression. - $3 - \sqrt { b }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 64 x ^ { 3 } } { 216 } \right) ^ { 4 / 3 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 1296 }$

Find the distance between the pair of points. - $( - 7 , - 2 )$ and $( 3 , - 6 )$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\sqrt { 529 }$

Find the distance between the pair of points. - $( 2,3 )$ and $( - 7 , - 5 )$

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 8 \sqrt { 3 } - 3 ) ^ { 2 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers

Use the Pythagorean theorem to find the unknown side of the right triangle. -

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

Perform the indicated operation. Write the result in the form a + bi. - 3+3i7−3i\frac { 3 + 3 i } { 7 - 3 i }7−3i3+3i​

Write with positive exponents. Simplify if possible. - 64−4/364 ^ { - 4 / 3 }64−4/3

Rationalize the denominator. Assume that all variables represent positive numbers. - 5x36y3\frac { \sqrt [ 3 ] { 5 x } } { \sqrt [ 3 ] { 6 y } }36y​35x​​

Find the square root. Assume that all variables represent positive real numbers. - 81x8\sqrt { 81 x ^ { 8 } }81x8​

Use the properties of exponents to simplify the expression. Write with positive exponents. - (b7)2/7\left( b ^ { 7 } \right) ^ { 2 / 7 }(b7)2/7

Use radical notation to write the expression. Simplify if possible. - (116)1/2\left( \frac { 1 } { 16 } \right) ^ { 1 / 2 }(161​)1/2

Use rational exponents to simplify the following. - y4z66\sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 6 } }6y4z6​

Use a calculator to approximate the number to three decimal places. - 356\sqrt { 356 }356​

Perform the indicated operation. Write the result in the form a + bi. - 2i(2−8i)2 \mathrm { i } ( 2 - 8 \mathrm { i } )2i(2−8i)

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - (43x1/4y5x1/4)1/3\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }(x1/443x1/4y5​)1/3

Write the conjugate of the expression. - 3−b3 - \sqrt { b }3−b​

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - (64x3216)4/3\left( \frac { 64 x ^ { 3 } } { 216 } \right) ^ { 4 / 3 }(21664x3​)4/3

Find the root. Assume that all variables represent nonnegative real numbers. - −12964- \sqrt [ 4 ] { 1296 }−41296​

Find the distance between the pair of points. - (−7,−2)( - 7 , - 2 )(−7,−2) and (3,−6)( 3 , - 6 )(3,−6)

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - 529\sqrt { 529 }529​

Find the distance between the pair of points. - (2,3)( 2,3 )(2,3) and (−7,−5)( - 7 , - 5 )(−7,−5)

Use the Pythagorean theorem to find the unknown side of the right triangle. -

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - (83−3)2( 8 \sqrt { 3 } - 3 ) ^ { 2 }(83​−3)2

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

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

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 3 + 3 i } { 7 - 3 i }$

Write with positive exponents. Simplify if possible. - $64 ^ { - 4 / 3 }$

Rationalize the denominator. Assume that all variables represent positive numbers. - $\frac { \sqrt [ 3 ] { 5 x } } { \sqrt [ 3 ] { 6 y } }$

Find the square root. Assume that all variables represent positive real numbers. - $\sqrt { 81 x ^ { 8 } }$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $\left( b ^ { 7 } \right) ^ { 2 / 7 }$

Use radical notation to write the expression. Simplify if possible. - $\left( \frac { 1 } { 16 } \right) ^ { 1 / 2 }$

Use rational exponents to simplify the following. - $\sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 6 } }$

Use a calculator to approximate the number to three decimal places. - $\sqrt { 356 }$

Perform the indicated operation. Write the result in the form a + bi. - $2 \mathrm { i } ( 2 - 8 \mathrm { i } )$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

Write the conjugate of the expression. - $3 - \sqrt { b }$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\left( \frac { 64 x ^ { 3 } } { 216 } \right) ^ { 4 / 3 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 1296 }$

Find the distance between the pair of points. - $( - 7 , - 2 )$ and $( 3 , - 6 )$

Raise to the power or find the root. Assume that all variables represent positive numbers. Write with only positive exponents. - $\sqrt { 529 }$

Find the distance between the pair of points. - $( 2,3 )$ and $( - 7 , - 5 )$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( 8 \sqrt { 3 } - 3 ) ^ { 2 }$