Simplify:
$ \left\{(-8)^{5} \div(-8)^{9}\right\} \times(-8)^{3} $

Given:

\( \left\{(-8)^{5} \div(-8)^{9}\right\} \times(-8)^{3} \)

To do:

We have to simplify \( \left\{(-8)^{5} \div(-8)^{9}\right\} \times(-8)^{3} \).

Solution:
We know that,

$a^m \times a^n=a^{m+n}$

$a^{m}\div a^{n}=a^{m-n}$

Therefore,

${(-8)^{5} \div(-8)^{9}} \times(-8)^{3}=(-8)^{5-9} \times (-8)^3$

$=(-8)^{-4}\times(-8)^3$

$=(-8)^{-4+3}$

$=(-8)^{-1}$

$=-\frac{1}{8}$

Hence, ${(-8)^{5} \div(-8)^{9}} \times(-8)^{3}=-\frac{1}{8}$.

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Updated on: 10-Oct-2022

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