Question 1

Perform the indicated operation and express your answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Accepted Answer

A)  $\sqrt [ 5 ] { 125 }$ 
B)  $\sqrt [ 5 ] { 3,125 }$ 
C)  $\sqrt [ 6 ] { 25 }$ 
D)  $\sqrt [ 6 ] { 5 }$ 
E)  $\sqrt [ 6 ] { 3,125 }$ 
A)  $\sqrt [ 5 ] { 125 }$ 
B)  $\sqrt [ 5 ] { 3,125 }$ 
C)  $\sqrt [ 6 ] { 25 }$ 
D)  $\sqrt [ 6 ] { 5 }$ 
E)  $\sqrt [ 6 ] { 3,125 }$ E

Question 2

Simplify the expression. $16 ^ { \frac { 3 } { 2 } }$

Accepted Answer

A) 16 
B) 7,776 
C) 36 
D) 11 
E) 1,024 
A) 16 
B) 7,776 
C) 36 
D) 11 
E) 1,024 A

Question 3

Simplify the expression. Express the final result without using zero or negative integers as exponents. $$a ^ { 4 } \cdot a ^ { - 5 } \cdot a ^ { - 2 }$$

Accepted Answer

A)  $\frac { a ^ { 4 } } { a ^ { 7 } }$ 
B)  $\frac { 1 } { a ^ { 3 } }$ 
C)  $\frac { 1 } { a ^ { 4 } }$ 
D)  $a$ 
E)  $\frac { a ^ { 4 } } { a ^ { 10 } }$ 
A)  $\frac { a ^ { 4 } } { a ^ { 7 } }$ 
B)  $\frac { 1 } { a ^ { 3 } }$ 
C)  $\frac { 1 } { a ^ { 4 } }$ 
D)  $a$ 
E)  $\frac { a ^ { 4 } } { a ^ { 10 } }$ B

Question 4

Simplify the expression. $\sqrt { 200 } + \sqrt { 700 } - \sqrt { 175 }$

Accepted Answer

A)  $10 \sqrt { 2 } - 5 \sqrt { 7 }$ 
B)  $10 \sqrt { 2 } + 5 \sqrt { 7 }$ 
C)  $2 \sqrt { 2 } + 5 \sqrt { 7 }$ 
D)  $5 \sqrt { 2 } + 2 \sqrt { 7 }$ 
E)  $2 \sqrt { 2 } - 5 \sqrt { 7 }$ 
A)  $10 \sqrt { 2 } - 5 \sqrt { 7 }$ 
B)  $10 \sqrt { 2 } + 5 \sqrt { 7 }$ 
C)  $2 \sqrt { 2 } + 5 \sqrt { 7 }$ 
D)  $5 \sqrt { 2 } + 2 \sqrt { 7 }$ 
E)  $2 \sqrt { 2 } - 5 \sqrt { 7 }$

Question 5

Simplify the expression. $\sqrt [ 3 ] { 128 x ^ { 4 } y ^ { 5 } } - \sqrt [ 3 ] { 54 x ^ { 4 } y ^ { 5 } }$

Accepted Answer

A)  $2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
B)  $- 2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
C)  $2 x ^ { 2 } y ^ { 3 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
D)  $- x y ^ { 2 } \sqrt [ 3 ] { 4 x y }$ 
E)  $x y \sqrt [ 3 ] { 2 x y ^ { 2 } }$ 
A)  $2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
B)  $- 2 x y ^ { 2 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
C)  $2 x ^ { 2 } y ^ { 3 } \sqrt [ 3 ] { 4 x y ^ { 2 } }$ 
D)  $- x y ^ { 2 } \sqrt [ 3 ] { 4 x y }$ 
E)  $x y \sqrt [ 3 ] { 2 x y ^ { 2 } }$

Question 6

Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

Accepted Answer

A)  $- 112 \sqrt { 77 } - 44 \sqrt { 7 } + 980 \sqrt { 11 } + 385$ 
B)  $112 \sqrt { 77 } - 44 \sqrt { 11 } - 980 \sqrt { 7 } + 385$ 
C)  $16 \sqrt { 7 } + 4 \sqrt { 11 } - 385$ 
D)  $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385 \sqrt { 343 }$ 
E)  $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385$ 
A)  $- 112 \sqrt { 77 } - 44 \sqrt { 7 } + 980 \sqrt { 11 } + 385$ 
B)  $112 \sqrt { 77 } - 44 \sqrt { 11 } - 980 \sqrt { 7 } + 385$ 
C)  $16 \sqrt { 7 } + 4 \sqrt { 11 } - 385$ 
D)  $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385 \sqrt { 343 }$ 
E)  $112 \sqrt { 77 } + 44 \sqrt { 7 } - 980 \sqrt { 11 } - 385$

Question 7

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.006)(110,000)

Accepted Answer

A) 6600 
B) 660 
C) 11.6 
D) 7100 
E) 710 
A) 6600 
B) 660 
C) 11.6 
D) 7100 
E) 710

Question 8

Simplify the radical. $\sqrt { 32 }$

Accepted Answer

A)  $4 \sqrt { 3 }$ 
B)  $5 \sqrt { 3 }$ 
C)  $16$ 
D)  $4 \sqrt { 2 }$ 
E)  $5 \sqrt { 2 }$ 
A)  $4 \sqrt { 3 }$ 
B)  $5 \sqrt { 3 }$ 
C)  $16$ 
D)  $4 \sqrt { 2 }$ 
E)  $5 \sqrt { 2 }$

Question 9

Simplify the expression. All variables represent positive numbers. $\sqrt { 2 x ^ { 3 } } - \sqrt { 18 x ^ { 3 } }$

Accepted Answer

A)  $- x \sqrt { 3 x }$ 
B)  $- x \sqrt { 2 x }$ 
C)  $- 2 x \sqrt { 2 x }$ 
D)  $- 2 x \sqrt { 3 x }$ 
E)  $- 2 x \sqrt { 5 x }$ 
A)  $- x \sqrt { 3 x }$ 
B)  $- x \sqrt { 2 x }$ 
C)  $- 2 x \sqrt { 2 x }$ 
D)  $- 2 x \sqrt { 3 x }$ 
E)  $- 2 x \sqrt { 5 x }$

Question 10

Use a calculator to find a rational approximation of the square root. Express your answer to the nearest hundredth. $\sqrt { 27 }$

Accepted Answer

A)  $2.60$ 
B)  $5.40$ 
C)  $5.20$ 
D)  $5.10$ 
E)  $10.39$ 
A)  $2.60$ 
B)  $5.40$ 
C)  $5.20$ 
D)  $5.10$ 
E)  $10.39$

Question 11

Multiply and simplify where possible. $( - 17 \sqrt { 17 } ) ( - 49 \sqrt { 343 } )$

Accepted Answer

A)  $5,831 \sqrt { 7 }$ 
B)  $833 \sqrt { 119 }$ 
C)  $17 \sqrt { 119 }$ 
D)  $5,831 \sqrt { 119 }$ 
E)  $343 \sqrt { 119 }$ 
A)  $5,831 \sqrt { 7 }$ 
B)  $833 \sqrt { 119 }$ 
C)  $17 \sqrt { 119 }$ 
D)  $5,831 \sqrt { 119 }$ 
E)  $343 \sqrt { 119 }$

Question 12

Write $- \sqrt [ 9 ] { x + y }$ using positive rational exponents.

Accepted Answer

A)  $- ( x + y ) ^ { 9 }$ 
B)  $( - x - y ) ^ { \frac { 1 } { 9 } }$ 
C)  $- ( x + y ) ^ { \frac { 2 } { 9 } }$ 
D)  $( x + y ) ^ { - \frac { 1 } { 9 } }$ 
E)  $- ( x + y ) ^ { \frac { 1 } { 9 } }$ 
A)  $- ( x + y ) ^ { 9 }$ 
B)  $( - x - y ) ^ { \frac { 1 } { 9 } }$ 
C)  $- ( x + y ) ^ { \frac { 2 } { 9 } }$ 
D)  $( x + y ) ^ { - \frac { 1 } { 9 } }$ 
E)  $- ( x + y ) ^ { \frac { 1 } { 9 } }$

Question 13

The distance from earth to a certain star outside our solar system is 25,800,000,000,000 miles. Express this number in scientific notation.

Accepted Answer

A)  $2.58 \times 10 ^ { - 13 }$ miles 
B)  $25.8 \times 10 ^ { - 12 }$ miles 
C)  $2.58 \times 10 ^ { 13 }$ miles 
D)  $2.58 \times 10 ^ { 12 }$ miles 
E)  $25.8 \times 10 ^ { 12 }$ miles 
A)  $2.58 \times 10 ^ { - 13 }$ miles 
B)  $25.8 \times 10 ^ { - 12 }$ miles 
C)  $2.58 \times 10 ^ { 13 }$ miles 
D)  $2.58 \times 10 ^ { 12 }$ miles 
E)  $25.8 \times 10 ^ { 12 }$ miles

Question 14

Simplify the expression. $\sqrt { 8 x y ^ { 3 } } - \sqrt { 75 y ^ { 3 } x }$

Accepted Answer

A)  $2 y ^ { 2 } \sqrt { 2 x y } - 5 y ^ { 2 } \sqrt { 3 x y }$ 
B)  $2 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$ 
C)  $3 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$ 
D)  $2 y \sqrt { 4 x y } - 5 y \sqrt { 15 x y }$ 
E) none of the above 
A)  $2 y ^ { 2 } \sqrt { 2 x y } - 5 y ^ { 2 } \sqrt { 3 x y }$ 
B)  $2 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$ 
C)  $3 y \sqrt { 2 x y } - 5 y \sqrt { 3 x y }$ 
D)  $2 y \sqrt { 4 x y } - 5 y \sqrt { 15 x y }$ 
E) none of the above

Question 15

Write $4 x ^ { \frac { 2 } { 7 } }$ in radical form. For example, $3 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }$

Accepted Answer

A)  $\frac { 1 } { 4 \sqrt [ 7 ] { x ^ { 2 } } }$ 
B)  $\sqrt { x ^ { 5 } }$ $\sqrt { x ^ { 7 } }$ 
C)  $4 \sqrt [ 7 ] { x ^ { 2 } }$ 
D)  $4 \sqrt [ 2 ] { x ^ { 7 } }$ 
E)  $\sqrt [ 7 ] { 4 x ^ { 2 } }$ 
A)  $\frac { 1 } { 4 \sqrt [ 7 ] { x ^ { 2 } } }$ 
B)  $\sqrt { x ^ { 5 } }$ $\sqrt { x ^ { 7 } }$ 
C)  $4 \sqrt [ 7 ] { x ^ { 2 } }$ 
D)  $4 \sqrt [ 2 ] { x ^ { 7 } }$ 
E)  $\sqrt [ 7 ] { 4 x ^ { 2 } }$

Question 16

Write the number $48.3 \times 10 ^ { 3 }$ in scientific notation.

Accepted Answer

A)  $483 \times 10 ^ { 2 }$ 
B) 48,300 
C)  $4.83 \times 10 ^ { 3 }$ 
D)  $4.83 \times 10 ^ { 4 }$ 
E)  $4.83 \times 10 ^ { 5 }$ 
A)  $483 \times 10 ^ { 2 }$ 
B) 48,300 
C)  $4.83 \times 10 ^ { 3 }$ 
D)  $4.83 \times 10 ^ { 4 }$ 
E)  $4.83 \times 10 ^ { 5 }$

Question 17

Simplify the numerical expression. $\left( 3 ^ { - 3 } + 5 ^ { - 2 } \right) ^ { - 1 }$

Accepted Answer

The answer of Simplify the numerical expression. \(\left( 3 ^...

Question 18

Write $2 \sqrt [ 13 ] { y ^ { 11 } }$ using positive rational exponents. For example, $\sqrt { a b } = ( a b ) ^ { \frac { 1 } { 2 } } = a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }$ .

Accepted Answer

A)  $4 y$ 
B)  $( 4 y ) ^ { \frac { 5 } { 13 } }$ 
C)  $y ^ { \frac { 5 } { 13 } }$ 
D)  $22 y ^ { 13 }$ 
E)  $4 y ^ { \frac { 13 } { 5 } }$ 
A)  $4 y$ 
B)  $( 4 y ) ^ { \frac { 5 } { 13 } }$ 
C)  $y ^ { \frac { 5 } { 13 } }$ 
D)  $22 y ^ { 13 }$ 
E)  $4 y ^ { \frac { 13 } { 5 } }$

Question 19

Simplify the expression by using the distributive property. $6 \sqrt { 11 } + 2 \sqrt { 11 }$

Accepted Answer

A)  $30$ 
B)  $12 \sqrt { 11 }$ 
C)  $8 \sqrt { 11 }$ 
D)  $4 \sqrt { 11 }$ 
E)  $7 \sqrt { 11 }$ 
A)  $30$ 
B)  $12 \sqrt { 11 }$ 
C)  $8 \sqrt { 11 }$ 
D)  $4 \sqrt { 11 }$ 
E)  $7 \sqrt { 11 }$

Question 20

Simplify the numerical expression. $$- 10 ^ { - 3 }$$

Accepted Answer

A)  $\frac { 1 } { 100 }$ 
B)  $- 1,000$ 
C)  $- \frac { 3 } { 1,000 }$ 
D)  $\frac { 1 } { 1,000 }$ 
E)  $- \frac { 1 } { 1,000 }$ 
A)  $\frac { 1 } { 100 }$ 
B)  $- 1,000$ 
C)  $- \frac { 3 } { 1,000 }$ 
D)  $\frac { 1 } { 1,000 }$ 
E)  $- \frac { 1 } { 1,000 }$

Perform the indicated operation and express your answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Simplify the expression. $16 ^ { \frac { 3 } { 2 } }$

Simplify the expression. Express the final result without using zero or negative integers as exponents. $a ^ { 4 } \cdot a ^ { - 5 } \cdot a ^ { - 2 }$

Simplify the expression. $\sqrt { 200 } + \sqrt { 700 } - \sqrt { 175 }$

Simplify the expression. $\sqrt [ 3 ] { 128 x ^ { 4 } y ^ { 5 } } - \sqrt [ 3 ] { 54 x ^ { 4 } y ^ { 5 } }$

Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.006)(110,000)

Simplify the radical. $\sqrt { 32 }$

Simplify the expression. All variables represent positive numbers. $\sqrt { 2 x ^ { 3 } } - \sqrt { 18 x ^ { 3 } }$

Use a calculator to find a rational approximation of the square root. Express your answer to the nearest hundredth. $\sqrt { 27 }$

Multiply and simplify where possible. $( - 17 \sqrt { 17 } ) ( - 49 \sqrt { 343 } )$

Write $- \sqrt [ 9 ] { x + y }$ using positive rational exponents.

The distance from earth to a certain star outside our solar system is 25,800,000,000,000 miles. Express this number in scientific notation.

Simplify the expression. $\sqrt { 8 x y ^ { 3 } } - \sqrt { 75 y ^ { 3 } x }$

Write $4 x ^ { \frac { 2 } { 7 } }$ in radical form. For example, $3 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }$

Write the number $48.3 \times 10 ^ { 3 }$ in scientific notation.

Simplify the numerical expression. $\left( 3 ^ { - 3 } + 5 ^ { - 2 } \right) ^ { - 1 }$

Write $2 \sqrt [ 13 ] { y ^ { 11 } }$ using positive rational exponents. For example, $\sqrt { a b } = ( a b ) ^ { \frac { 1 } { 2 } } = a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }$ .

Simplify the expression by using the distributive property. $6 \sqrt { 11 } + 2 \sqrt { 11 }$

Simplify the numerical expression. $- 10 ^ { - 3 }$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 5: Exponents and Radicals

Perform the indicated operation and express your answer in simplest radical form. 553\sqrt { 5 } \sqrt [ 3 ] { 5 }5​35​

Simplify the expression. 163216 ^ { \frac { 3 } { 2 } }1623​

Simplify the expression. Express the final result without using zero or negative integers as exponents. a4⋅a−5⋅a−2a ^ { 4 } \cdot a ^ { - 5 } \cdot a ^ { - 2 }a4⋅a−5⋅a−2

Simplify the expression. 200+700−175\sqrt { 200 } + \sqrt { 700 } - \sqrt { 175 }200​+700​−175​

Simplify the expression. 128x4y53−54x4y53\sqrt [ 3 ] { 128 x ^ { 4 } y ^ { 5 } } - \sqrt [ 3 ] { 54 x ^ { 4 } y ^ { 5 } }3128x4y5​−354x4y5​

Find the following product and express your answer in simplest radical form. (411−577)(4343+77)( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )(411​−577​)(4343​+77​)

Use scientific notation and the properties of exponents to help you perform the following operation. Express the answer in ordinary decimal notation. (0.006)(110,000)

Simplify the radical. 32\sqrt { 32 }32​

Simplify the expression. All variables represent positive numbers. 2x3−18x3\sqrt { 2 x ^ { 3 } } - \sqrt { 18 x ^ { 3 } }2x3​−18x3​

Use a calculator to find a rational approximation of the square root. Express your answer to the nearest hundredth. 27\sqrt { 27 }27​

Multiply and simplify where possible. (−1717)(−49343)( - 17 \sqrt { 17 } ) ( - 49 \sqrt { 343 } )(−1717​)(−49343​)

Write −x+y9- \sqrt [ 9 ] { x + y }−9x+y​ using positive rational exponents.

The distance from earth to a certain star outside our solar system is 25,800,000,000,000 miles. Express this number in scientific notation.

Simplify the expression. 8xy3−75y3x\sqrt { 8 x y ^ { 3 } } - \sqrt { 75 y ^ { 3 } x }8xy3​−75y3x​

Write 4x274 x ^ { \frac { 2 } { 7 } }4x72​ in radical form. For example, 3x23=3x233 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }3x32​=33x2​

Write the number 48.3×10348.3 \times 10 ^ { 3 }48.3×103 in scientific notation.

Simplify the numerical expression. (3−3+5−2)−1\left( 3 ^ { - 3 } + 5 ^ { - 2 } \right) ^ { - 1 }(3−3+5−2)−1

Write 2y11132 \sqrt [ 13 ] { y ^ { 11 } }213y11​ using positive rational exponents. For example, ab=(ab)12=a12b12\sqrt { a b } = ( a b ) ^ { \frac { 1 } { 2 } } = a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }ab​=(ab)21​=a21​b21​ .

Simplify the expression by using the distributive property. 611+2116 \sqrt { 11 } + 2 \sqrt { 11 }611​+211​

Simplify the numerical expression. −10−3- 10 ^ { - 3 }−10−3

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

Rational Expressions

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Perform the indicated operation and express your answer in simplest radical form. $\sqrt { 5 } \sqrt [ 3 ] { 5 }$

Simplify the expression. $16 ^ { \frac { 3 } { 2 } }$

Simplify the expression. Express the final result without using zero or negative integers as exponents. $a ^ { 4 } \cdot a ^ { - 5 } \cdot a ^ { - 2 }$

Simplify the expression. $\sqrt { 200 } + \sqrt { 700 } - \sqrt { 175 }$

Simplify the expression. $\sqrt [ 3 ] { 128 x ^ { 4 } y ^ { 5 } } - \sqrt [ 3 ] { 54 x ^ { 4 } y ^ { 5 } }$

Find the following product and express your answer in simplest radical form. $( 4 \sqrt { 11 } - 5 \sqrt { 77 } ) ( 4 \sqrt { 343 } + \sqrt { 77 } )$

Simplify the radical. $\sqrt { 32 }$

Simplify the expression. All variables represent positive numbers. $\sqrt { 2 x ^ { 3 } } - \sqrt { 18 x ^ { 3 } }$

Use a calculator to find a rational approximation of the square root. Express your answer to the nearest hundredth. $\sqrt { 27 }$

Multiply and simplify where possible. $( - 17 \sqrt { 17 } ) ( - 49 \sqrt { 343 } )$

Write $- \sqrt [ 9 ] { x + y }$ using positive rational exponents.

Simplify the expression. $\sqrt { 8 x y ^ { 3 } } - \sqrt { 75 y ^ { 3 } x }$

Write $4 x ^ { \frac { 2 } { 7 } }$ in radical form. For example, $3 x ^ { \frac { 2 } { 3 } } = 3 \sqrt [ 3 ] { x ^ { 2 } }$

Write the number $48.3 \times 10 ^ { 3 }$ in scientific notation.

Simplify the numerical expression. $\left( 3 ^ { - 3 } + 5 ^ { - 2 } \right) ^ { - 1 }$

Write $2 \sqrt [ 13 ] { y ^ { 11 } }$ using positive rational exponents. For example, $\sqrt { a b } = ( a b ) ^ { \frac { 1 } { 2 } } = a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } }$ .

Simplify the expression by using the distributive property. $6 \sqrt { 11 } + 2 \sqrt { 11 }$

Simplify the numerical expression. $- 10 ^ { - 3 }$