Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{2}{3}}}{z^{\frac{4}{3}}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

View step-by-step help

View step-by-step help

Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{2}{3}}}{z^{\frac{4}{3}}}

\newline

Write your answer in the form

A

or

\frac{A}{B}

, where

A

and

B

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

\newline

______

Identify Operation: Identify the operation to be applied with the exponents. $\newline$ When dividing powers with the same base, subtract the exponents.
Apply Exponent Rule: Apply the exponent subtraction rule to simplify the expression. $\newline$ $\frac{z^{\frac{2}{3}}}{z^{\frac{4}{3}}} = z^{\left(\frac{2}{3}-\frac{4}{3}\right)} = z^{-\frac{2}{3}}$
Rewrite with Positive Exponent: Since we want the exponent to be positive, rewrite the expression with a positive exponent. $\newline$ $z^{(-\frac{2}{3})} = \frac{1}{z^{(\frac{2}{3})}}$

More problems from Division with rational exponents

Question

\newline

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

\newline

Posted 2 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 2 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 1 month 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 1 month ago

Question

\newline

32^{(-1/5)}

Posted 1 month 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 2 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 2 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 1 month ago