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

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

______

Multiply powers with same base: When multiplying powers with the same base, we add the exponents. So we add the exponents $\frac{6}{5}$ and $\frac{7}{5}$ . $\newline$ $b^{\frac{6}{5}} \times b^{\frac{7}{5}} = b^{\left(\frac{6}{5} + \frac{7}{5}\right)}$
Calculate sum of exponents: Calculate the sum of the exponents. $\newline$ $(\frac{6}{5}) + (\frac{7}{5}) = (\frac{6 + 7}{5}) = \frac{13}{5}$
Write result as single power: Write the result as a single power of $b$ . $b^{\frac{6}{5}} \times b^{\frac{7}{5}} = b^{\frac{13}{5}}$

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