Question

Simplify and write $\frac{{(-2)}^{10}\times {(-2)}^3\times {(-2)}^5}{{(-2)}^7}$ as a single exponent.

Answer 1

We know that for any non-zero integers $\text{'}a\text{'}$ and natural numbers $m$ and $n$, we have :

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

$\frac{a^m}{a^n}=a^{m-n}$

So, $\frac{{(-2)}^{10}\times {(-2)}^3\times {(-2)}^5}{{(-2)}^7}$$=\frac{{(-2)}^{10+3+5}}{{(-2)}^7}=\frac{{(-2)}^{18}}{{(-2)}^7}={(-2)}^{18-7}={(-2)}^{11}$

Hence, $\frac{{(-2)}^{10}\times {(-2)}^3\times {(-2)}^5}{{(-2)}^7}$ can be written as ${(-2)}^{11}$.