Question

Fill in the blanks to make the statement true: ${(-2)}^{31}\times {(-2)}^{13}={(-2)}^{\_\_\_\_\_\_}$.

Answer 1

Simplifying the given expression:

Given: ${(-2)}^{31}\times {(-2)}^{13}={(-2)}^{\_\_\_\_\_\_}$

To solve this we need the formula

$a^m\times a^n=a^{m+n}$

So by using the formula

$\begin{array}{rcl}& =& {(-2)}^{31}\times {(-2)}^{13}\\ & =& {(-2)}^{31+13}\\ & =& -2^{44}\end{array}$

Hence the required answer is $44$.