Question 1

Solve the equation. Check all solutions. $\sqrt { x } = 9$

Accepted Answer

A) 81 
B) 41 
C) 9 
D) 79 
E) no solution 
A) 81 
B) 41 
C) 9 
D) 79 
E) no solution

Question 2

Use scientific notation and the rules for exponents to simplify the following expression. Express your answer in standard notation. $\left( 7.6 \times 10 ^ { 2 } \right) \left( 2.6 \times 10 ^ { 3 } \right)$

Accepted Answer

A) 1,976,000 
B) 197,600 
C) 1,976,000,000 
D) 197,600,000 
E) 19,760,000 
A) 1,976,000 
B) 197,600 
C) 1,976,000,000 
D) 197,600,000 
E) 19,760,000

Question 3

Find the following product and express your answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Accepted Answer

A)  $\sqrt { 5 } - \sqrt { 3 }$ 
B)  $\sqrt { 3 } - 7$ 
C)  $\sqrt { 5 } + \sqrt { 7 }$ 
D)  $\sqrt { 15 } + \sqrt { 35 }$ 
E)  $\sqrt { 15 } - \sqrt { 35 }$ 
A)  $\sqrt { 5 } - \sqrt { 3 }$ 
B)  $\sqrt { 3 } - 7$ 
C)  $\sqrt { 5 } + \sqrt { 7 }$ 
D)  $\sqrt { 15 } + \sqrt { 35 }$ 
E)  $\sqrt { 15 } - \sqrt { 35 }$

Question 4

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 14 } } { \sqrt [ 3 ] { 7 } }$

Accepted Answer

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

Question 5

The power generated by a windmill is related to the speed of the wind by the formula $S = \sqrt [ 3 ] { \frac { P } { 0.02 } }$ , where $S$ is the speed of the wind (in mph)and $P$ is the power (in watts). Find the speed of the wind when the windmill is producing 413 watts of power.

Accepted Answer

A) 27.07 mph 
B) 28.99 mph 
C) 28.25 mph 
D) 27.44 mph 
E) 27.56 mph 
A) 27.07 mph 
B) 28.99 mph 
C) 28.25 mph 
D) 27.44 mph 
E) 27.56 mph

Question 6

Simplify the expression. $\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$

Accepted Answer

A)  $- \frac { 81 } { 256 }$ 
B)  $- \frac { 3 } { 4 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $- \frac { 243 } { 4 }$ 
E)  $- \frac { 5 } { 6 }$ 
A)  $- \frac { 81 } { 256 }$ 
B)  $- \frac { 3 } { 4 }$ 
C)  $- \frac { 4 } { 3 }$ 
D)  $- \frac { 243 } { 4 }$ 
E)  $- \frac { 5 } { 6 }$

Question 7

Find the following product and express your answer in simplest radical form. $\frac { \sqrt { 42 } } { 7 \sqrt { 6 } + 6 \sqrt { 7 } }$

Accepted Answer

A)  $\sqrt { 6 } - \sqrt { 7 }$ 
B)  $\sqrt { 7 } - \sqrt { 6 }$ 
C)  $\frac { \sqrt { 42 } } { \sqrt { 7 } + \sqrt { 6 } }$ 
D)  $\sqrt { 7 } + \sqrt { 6 }$ 
E)  $\frac { 1 } { \sqrt { 7 } + \sqrt { 6 } }$ 
A)  $\sqrt { 6 } - \sqrt { 7 }$ 
B)  $\sqrt { 7 } - \sqrt { 6 }$ 
C)  $\frac { \sqrt { 42 } } { \sqrt { 7 } + \sqrt { 6 } }$ 
D)  $\sqrt { 7 } + \sqrt { 6 }$ 
E)  $\frac { 1 } { \sqrt { 7 } + \sqrt { 6 } }$

Question 8

Write the number 0.00061 in scientific notation.

Accepted Answer

A)  $61 \times 10 ^ { - 4 }$ 
B)  $6.1 \times 10 ^ { - 6 }$ 
C)  $61 \times 10 ^ { - 5 }$ 
D)  $6.1 \times 10 ^ { - 4 }$ 
E)  $6.1 \times 10 ^ { - 5 }$ 
A)  $61 \times 10 ^ { - 4 }$ 
B)  $6.1 \times 10 ^ { - 6 }$ 
C)  $61 \times 10 ^ { - 5 }$ 
D)  $6.1 \times 10 ^ { - 4 }$ 
E)  $6.1 \times 10 ^ { - 5 }$

Question 9

Express the following as a single fraction involving positive exponents only. $$- 4 x ^ { - 3 } - 5 x ^ { - 7 } + x$$

Accepted Answer

A)  $\frac { x ^ { 6 } - 4 x ^ { 4 } - 5 } { x ^ { 7 } }$ 
B)  $- \frac { x } { 4 x ^ { 7 } + 5 x ^ { 3 } }$ 
C)  $\frac { 4 x ^ { 4 } + 5 } { x ^ { 6 } }$ 
D)  $x ^ { 6 } - 4 x ^ { 7 } - 5 x ^ { 3 }$ 
E)  $- \frac { 1 } { x ^ { 10 } }$ 
A)  $\frac { x ^ { 6 } - 4 x ^ { 4 } - 5 } { x ^ { 7 } }$ 
B)  $- \frac { x } { 4 x ^ { 7 } + 5 x ^ { 3 } }$ 
C)  $\frac { 4 x ^ { 4 } + 5 } { x ^ { 6 } }$ 
D)  $x ^ { 6 } - 4 x ^ { 7 } - 5 x ^ { 3 }$ 
E)  $- \frac { 1 } { x ^ { 10 } }$

Solve the equation. Check all solutions. $\sqrt { x } = 9$

Use scientific notation and the rules for exponents to simplify the following expression. Express your answer in standard notation. $\left( 7.6 \times 10 ^ { 2 } \right) \left( 2.6 \times 10 ^ { 3 } \right)$

Find the following product and express your answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 14 } } { \sqrt [ 3 ] { 7 } }$

The power generated by a windmill is related to the speed of the wind by the formula $S = \sqrt [ 3 ] { \frac { P } { 0.02 } }$ , where $S$ is the speed of the wind (in mph)and $P$ is the power (in watts). Find the speed of the wind when the windmill is producing 413 watts of power.

Simplify the expression. $\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$

Find the following product and express your answer in simplest radical form. $\frac { \sqrt { 42 } } { 7 \sqrt { 6 } + 6 \sqrt { 7 } }$

Write the number 0.00061 in scientific notation.

Express the following as a single fraction involving positive exponents only. $- 4 x ^ { - 3 } - 5 x ^ { - 7 } + x$

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Polynomials

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Exam 5: Exponents and Radicals

Solve the equation. Check all solutions. x=9\sqrt { x } = 9x​=9

Use scientific notation and the rules for exponents to simplify the following expression. Express your answer in standard notation. (7.6×102)(2.6×103)\left( 7.6 \times 10 ^ { 2 } \right) \left( 2.6 \times 10 ^ { 3 } \right)(7.6×102)(2.6×103)

Find the following product and express your answer in simplest radical form. All variables represent nonnegative real numbers. 5(3+7)\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )5​(3​+7​)

Change the radical to simplest radical form. 14373\frac { \sqrt [ 3 ] { 14 } } { \sqrt [ 3 ] { 7 } }37​314​​

Simplify the expression. (−2431024)15\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }(−1024243​)51​

Find the following product and express your answer in simplest radical form. 4276+67\frac { \sqrt { 42 } } { 7 \sqrt { 6 } + 6 \sqrt { 7 } }76​+67​42​​

Write the number 0.00061 in scientific notation.

Express the following as a single fraction involving positive exponents only. −4x−3−5x−7+x- 4 x ^ { - 3 } - 5 x ^ { - 7 } + x−4x−3−5x−7+x

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

Solve the equation. Check all solutions. $\sqrt { x } = 9$

Use scientific notation and the rules for exponents to simplify the following expression. Express your answer in standard notation. $\left( 7.6 \times 10 ^ { 2 } \right) \left( 2.6 \times 10 ^ { 3 } \right)$

Find the following product and express your answer in simplest radical form. All variables represent nonnegative real numbers. $\sqrt { 5 } ( \sqrt { 3 } + \sqrt { 7 } )$

Change the radical to simplest radical form. $\frac { \sqrt [ 3 ] { 14 } } { \sqrt [ 3 ] { 7 } }$

Simplify the expression. $\left( - \frac { 243 } { 1024 } \right) ^ { \frac { 1 } { 5 } }$

Find the following product and express your answer in simplest radical form. $\frac { \sqrt { 42 } } { 7 \sqrt { 6 } + 6 \sqrt { 7 } }$

Express the following as a single fraction involving positive exponents only. $- 4 x ^ { - 3 } - 5 x ^ { - 7 } + x$