Simplify the following:$(-\frac{1}{3})^{4} \div(-\frac{1}{3})^{8} \times(-\frac{1}{3})^{5}$.

Given :

The given expression is $(-\frac{1}{3})^{4} \div(-\frac{1}{3})^{8} \times(-\frac{1}{3})^{5}$.

To do :

We have to simplify the given expression.

Solution :

$(-\frac{1}{3})^{4} \div(-\frac{1}{3})^{8} \times(-\frac{1}{3})^{5}$

$\Rightarrow (-\frac{1}{3})^{4-8} \times(-\frac{1}{3})^{5}$       $[a^m \div a^n = a^{m-n}]$

$\Rightarrow (-\frac{1}{3})^{-4} \times(-\frac{1}{3})^{5}$  

$\Rightarrow (-\frac{1}{3})^{-4+5}$                    $[a^m \times a^n=a^{m+n}]$

$\Rightarrow (-\frac{1}{3})^{1}=-\frac{1}{3}$

Therefore, the value of $(-\frac{1}{3})^{4} \div(-\frac{1}{3})^{8} \times(-\frac{1}{3})^{5}$ is $-\frac{1}{3}$.

$\left(\frac{-1}{3}\right)^{4} \div \left(\frac{-1}{3}\right)^{8} \times \left(\frac{-1}{3}\right)^{5}$

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Updated on: 10-Oct-2022

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