Question

Write ${\left(\frac{5}{4}\right)}^9÷{\left(\frac{5}{4}\right)}^5$ as a single exponent.

Answer 1

As we know that for any non-zero integer $\text{'}a\text{'}$ and natural numbers $m$ and $n$ where $m>n$, we have;

$\frac{a^m}{a^n}=a^{m-n}$, i.e., we will subtract the powers in case we have same base and different powers in the division.

So, according to this,${\left(\frac{5}{4}\right)}^9÷{\left(\frac{5}{4}\right)}^5$$={\left(\frac{5}{4}\right)}^{9-5}={\left(\frac{5}{4}\right)}^4$.

Hence, ${\left(\frac{5}{4}\right)}^9÷{\left(\frac{5}{4}\right)}^5$ as a single exponent will be equal to ${\left(\frac{5}{4}\right)}^4$.