Question

simplify
(\frac{-8y^{3}}{x})^{2}
write your answer without parentheses.

Explanation:

Step1: Apply power - of - a - quotient rule

$(\frac{-8y^{3}}{x})^{2}=\frac{(-8y^{3})^{2}}{x^{2}}$

Step2: Apply power - of - a - product rule to $(-8y^{3})^{2}$

$(-8y^{3})^{2}=(-8)^{2}(y^{3})^{2}$
Since $(-8)^{2}=64$ and $(y^{3})^{2}=y^{3\times2}=y^{6}$, then $(-8y^{3})^{2}=64y^{6}$

Step3: Combine the results

$\frac{(-8y^{3})^{2}}{x^{2}}=\frac{64y^{6}}{x^{2}}$

Answer:

$\frac{64y^{6}}{x^{2}}$