Question

$\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}$ can be rewritten as:

• A. $a^{p-m+n}$
• B. $a^{m+n-p}$
• C. $a^{mnp}$
• D. $a^{p-mn}$

Answer 1

The correct option is B $a^{m+n-p}$

We know that $a^m$ $\times$ $a^n=a^{m+n}$

So, $\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}$ = $\frac{\left(a^{m+n}\right)}{\left(a^p\right)}$

and also, $\frac{\left(a^m\right)}{\left(a^n\right)}=a^{m-n}$

$\Rightarrow \frac{\left(a^{m+n}\right)}{\left(a^p\right)}=a^{m+n-p}$

Therefore, $\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}=a^{m+n-p}$