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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 $-\frac{1}{3}$.
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