Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. $\newline$ $(-32)^{1/5}$ $\newline$ ______

View step-by-step help

View step-by-step help

Evaluate integers raised to rational exponents

Full solution

Q. Simplify.

\newline

(-32)^{1/5}

\newline

______

Recognize exponent as fifth root: We need to simplify the expression $(-32)^{\frac{1}{5}}$ . $\newline$ First, we recognize that the exponent $\frac{1}{5}$ represents the fifth root.
Apply exponent rule: We can apply the exponent rule that states $(-a)^{\frac{1}{n}} = - (a)^{\frac{1}{n}}$ for any positive real number $a$ and positive integer $n$ . $\newline$ So, $(-32)^{\frac{1}{5}} = -(32)^{\frac{1}{5}}$ .
Find fifth root of $32$ : Now we need to find the fifth root of $32$ . $\newline$ We know that $2^5 = 32$ , so the fifth root of $32$ is $2$ .
Replace expression with result: Therefore, we can replace $(32)^{1/5}$ with $2$ . $\newline$ So, $(-32)^{1/5}$ = $-2$ .

More problems from Evaluate integers raised to rational exponents

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 6 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 2 months ago

Question

\newline

32^{(-1/5)}

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 6 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 6 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 5 months ago

Question

4

Posted 17 hours ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant