Question

Write ${\left(\frac{-3}{4}\right)}^2\times {\left(\frac{-3}{4}\right)}^5$ as a single exponent.

Answer 1

We know that for any non-zero integer $a$ and natural numbers $m$ and $n$, we have , $a^m\times a^n=a^{m+n}$.

Also, in other words, powers will get added when base is same and powers are different.

In ${\left(\frac{-3}{4}\right)}^2\times {\left(\frac{-3}{4}\right)}^5$, we have same base $\frac{-3}{4}$ and different powers, so, we will add the powers.

Thus, ${\left(\frac{-3}{4}\right)}^2\times {\left(\frac{-3}{4}\right)}^5$$={\left(\frac{-3}{4}\right)}^{2+5}={\left(\frac{-3}{4}\right)}^7$.

Hence, ${\left(\frac{-3}{4}\right)}^2\times {\left(\frac{-3}{4}\right)}^5$ as a single exponent is ${\left(\frac{-3}{4}\right)}^7$.