Question

Can I get some help, I dont know how to do this and cant figure it out

Answer 1

9514 1404 393

Answer:

121x^3/y^3

Explanation:

It helps to understand a couple of rules of exponents:

(a/b)^c = (a^c)/(b^c)

1/a^-b = a^b

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The number that multiplies the variable expression can be found using your calculator.

(4^2 -27)^2 = (16 -27)^2 = (-11)^2 = 121

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For a moment, consider making the substitution ...

z = x/y

Then the expression becomes ...

121 ÷ z^(-3)

We know from our understanding of division that this is ...

`=121*(1)/(z^(-3))\\\\=121z^3\qquad\text{using the rule for negative exponents}\\\\=121\left((x)/(y)\right)^3\qquad\text{replacing z with x/y}\\\\=\boxed{(121x^3)/(y^3)}\qquad\text{using the rule for power of a fraction}`