Respuesta :
we are given
[tex]\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]
step-1:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:\frac{1}{x^{b-a}}[/tex]
[tex]\frac{p^{-4}}{p^{-3}}=\frac{1}{p^{-3-\left(-4\right)}}=\frac{1}{p}[/tex]
[tex]=\frac{q^5r^6}{pqr^{-2}}[/tex]
step-2:
[tex]\mathrm{Cancel\:the\:common\:factor:}\:q[/tex]
[tex]=\frac{q^4r^6}{pr^{-2}}[/tex]
step-3:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}[/tex]
[tex]\frac{r^6}{r^{-2}}=r^{6-\left(-2\right)}=r^8[/tex]
[tex]=\frac{q^4r^8}{p}[/tex]
so, we get
[tex]\frac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}=\frac{q^4r^8}{p} [/tex].............Answer
Answer:
p^-1q^5r^8
Step-by-step explanation:
so we have p^-4q^5r^6/p^-3qr^-2
first:p^-4/p^-3 so leave the p alone and do -4--3( when a negative number is after the minus sign it becomes a positive) so it becomes -4+3=-1
so we have p^-1
then q^5/q so do 5-1=4 (when you just have a letter it automatically has ^1) so q^4
then we have r^6/r^-2(same rule applies to r as p)
so do 6+2=8
put it together and the answer is p^-1q^5r^8
