Question

100 POINTS!!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Multiply or divide as indicated. Leave your answer with no factors in the denominator.

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

Answer 1

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

Explanation:

Given expression:

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

Separate the variables:

`\implies(p^(-4))/(p^(-3)) * (q^5)/(q) * (r^6)/(r^(-2))`

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

`\implies p^((-4-(-3)) * q^((5-1)) * r^((6-(-2))`

`\implies p^((-4+3)) * q^((5-1)) * r^((6+2))`

`\implies p^(-1) * q^(4) * r^8`

`\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (1)/(p) * q^(4) * r^8`

Simplify:

`\implies (q^(4) * r^8)/(p)`

`\implies (q^(4) r^8)/(p)`