Question

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

Answer 1

p^-1q^5r^8

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

Answer 2

we are given

`(p^(-4)q^5r^6)/(p^(-3)qr^(-2))`

step-1:

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)\:=\:(1)/(x^(b-a))`

`(p^(-4))/(p^(-3))=(1)/(p^(-3-\left(-4\right)))=(1)/(p)`

`=(q^5r^6)/(pqr^(-2))`

step-2:

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

`=(q^4r^6)/(pr^(-2))`

step-3:

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)\:=\:x^(a-b)`

`(r^6)/(r^(-2))=r^(6-\left(-2\right))=r^8`

`=(q^4r^8)/(p)`

so, we get

`(p^(-4)q^5r^6)/(p^(-3)qr^(-2))=(q^4r^8)/(p)`.............Answer