Question

Represent $\frac{3^5}{{\left(-4\right)}^5}$ as a single exponent.

Answer 1

We know that for any non-zero integers $\text{'}a\text{'}$ and $\text{'}b\text{'}$ and for any natural number $\text{'}n\text{'}$, we have, $\frac{a^n}{b^n}={\left(\frac{a}{b}\right)}^n$.

So, on applying, we get:$\frac{3^5}{{\left(-4\right)}^5}$$={\left(\frac{3}{-4}\right)}^5$

Hence, $\frac{3^5}{{\left(-4\right)}^5}$ as a single exponent is equal to ${\left(\frac{3}{-4}\right)}^5$.