Question

Please help with the question below!

Answer 1

We check to verify that the step
`(x^(-3)y^(-12))/(x^(15)y^(-15))` is included in simplifying the expression.

Thus, option D is correct.

Explanation:

Given the expression

`\left((xy^4)/(x^(-5)y^5)\right)^(-3)`

`\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)`

`=(x^(-3)y^(-12))/(x^(15)y^(-15))` ← This is the step

Thus, the step
`(x^(-3)y^(-12))/(x^(15)y^(-15))` is included in simplifying the expression.

Thus, option D is correct.

BONUS!

LET US SOLVE THE REMAINING

`=(x^(-3)y^(-12))/(x^(15)y^(-15))`

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

`=(y^(-12))/(y^(-15)x^(15-\left(-3\right)))`

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

`=(y^(-12-\left(-15\right)))/(x^(18))`

`=(y^3)/(x^(18))`

From the above calculations, we check to verify that the step
`(x^(-3)y^(-12))/(x^(15)y^(-15))` is included in simplifying the expression.

Thus, option D is correct.