Question

Simplify $\left[\left\{{\left(\frac{-2}{5}\right)}^{-7}\times {\left(\frac{-2}{5}\right)}^9\right\}÷{\left(\frac{-2}{5}\right)}^2\right]$ and express the result as a power of $5.$

Answer 1

$[\{{\left(\frac{-2}{5}\right)}^{-7}\times {\left(\frac{-2}{5}\right)}^9\}÷{\left(\frac{-2}{5}\right)}^2]$

$\Rightarrow$ ${\left(\frac{-2}{5}\right)}^{-7+9}÷{\left(\frac{-2}{5}\right)}^2$ [ $a^m\times a^n=a^{m+n}$ ]

$\Rightarrow$ ${\left(\frac{-2}{5}\right)}^2÷{\left(\frac{-2}{5}\right)}^2$

$\Rightarrow$ ${\left(\frac{-2}{5}\right)}^{2-2}$ [ $a^m÷a^n=a^{m-n}$ ]

$\Rightarrow$ ${\left(\frac{-2}{5}\right)}^0$

$\Rightarrow$ $1$

$\Rightarrow$ $1^5$