Answer
$\frac{1}{8y^{12}}$
Work Step by Step
We start with the given expression: $(2y^{4})^{-3}$
To raise a product to a power, we raise each factor to the power and multiply: $2^{-3}(y^{4})^{-3}$
To raise a power to a power, we multiply the exponents: $2^{-3}y^{-12}$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{1}{2^3y^{12}}$
We expand the exponent in the denominator: $\frac{1}{2^3y^{12}}=\frac{1}{2\times2\times2y^{12}}=\frac{1}{8y^{12}}$
