9514 1404 393
Answer:
121x^3/y^3
Step-by-step 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 ...
[tex]=121\times\dfrac{1}{z^{-3}}\\\\=121z^3\qquad\text{using the rule for negative exponents}\\\\=121\left(\dfrac{x}{y}\right)^3\qquad\text{replacing z with x/y}\\\\=\boxed{\dfrac{121x^3}{y^3}}\qquad\text{using the rule for power of a fraction}[/tex]
