Question

Divide p^-4q^5r^6/p^-3qr^-2

Answer 1

we are given

$\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}$

step-1:

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:\frac{1}{x^{b-a}}$

$\frac{p^{-4}}{p^{-3}}=\frac{1}{p^{-3-\left(-4\right)}}=\frac{1}{p}$

$=\frac{q^5r^6}{pqr^{-2}}$

step-2:

$\mathrm{Cancel\:the\:common\:factor:}\:q$

$=\frac{q^4r^6}{pr^{-2}}$

step-3:

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

$\frac{r^6}{r^{-2}}=r^{6-\left(-2\right)}=r^8$

$=\frac{q^4r^8}{p}$

so, we get

$\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}=\frac{q^4r^8}{p}$.............Answer