Question

simplify. write the answer using positive exponents only.
\left(\frac{x^{-4}}{x^{-2}}\
ight)^{-4}

\left(\frac{x^{-4}}{x^{-2}}\
ight)^{-4} = \square

Explanation:

Step1: Subtract exponents in fraction

When dividing like bases, subtract exponents: $x^{m-n}$.
$\frac{x^{-4}}{x^{-2}} = x^{-4 - (-2)} = x^{-2}$

Step2: Apply power of a power rule

Raise the result to the -4 power: $(x^a)^b = x^{a \cdot b}$.
$(x^{-2})^{-4} = x^{(-2) \times (-4)} = x^{8}$

Answer:

$x^{8}$