Question

Write ${(-3)}^4\times {(-3)}^6$ 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 ${(-3)}^4\times {(-3)}^6$, we have same base $(-3)$ and different powers, so , we will add the powers.

Thus, ${(-3)}^4\times {(-3)}^6$$={(-3)}^{4+6}={(-3)}^{10}$.

Hence, ${(-3)}^4\times {(-3)}^6$ as a single exponent is ${(-3)}^{10}$.