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Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{6}{5}}}{b^{\frac{7}{5}}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{b^{\frac{6}{5}}}{b^{\frac{7}{5}}}

\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

______

Combine powers of $b$ : Write $b^{\frac{6}{5}} / b^{\frac{7}{5}}$ as a single power of $b$ . $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $b^{\frac{6}{5}} / b^{\frac{7}{5}}$ $\newline$ = $b^{\left(\frac{6}{5}-\frac{7}{5}\right)}$ $\newline$ = $b^{-\frac{1}{5}}$
Negative exponent rule: Express $b^{-1/5}$ with a positive exponent. $\newline$ According to the negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $b^{-1/5} = \frac{1}{b^{1/5}}$

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