Question

Write the following in exponential form assuming denominators not equal to zero:

$\frac{{(-5)}^{10}}{{(-5)}^4}$

Answer 1

For any non-zero integer $a$, where $m$ and $n$ are whole numbers and $m>n$.

$a^m÷a^n=\frac{a^m}{a^n}=a^{m-n}$

So, $\frac{{(-5)}^{10}}{{(-5)}^4}$$={(-5)}^{10-4}$ where $a=-5,m=10,n=4$

$={(-5)}^6$.

Therefore, $\frac{{(-5)}^{10}}{{(-5)}^4}$$={(-5)}^6$.