Question

Simplify and write ${\left(\frac{-3}{5}\right)}^7÷{\left(\frac{-3}{5}\right)}^4$as a single exponent.

Answer 1

As we know for any non-zero integer $\text{'}a\text{'}$ and natural numbers $m$ and $n$, $\frac{a^m}{a^n}=a^{m-n}$.

In other words, if the base is the same and powers are different in the division, the exponents get subtracted.

Applying the same, ${\left(\frac{-3}{5}\right)}^7÷{\left(\frac{-3}{5}\right)}^4$$={\left(\frac{-3}{5}\right)}^{7-4}={\left(\frac{-3}{5}\right)}^3$

Hence,${\left(\frac{-3}{5}\right)}^7÷{\left(\frac{-3}{5}\right)}^4$ is equal to ${\left(\frac{-3}{5}\right)}^3$.