Simplify (x^-2)/((x^2)^-4)

$\frac{x^{- 2}}{{(x^{2})}^{- 4}}$

Simplify the expression.

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x^{2})}^{- 4} x^{2}}$

Move ${(x^{2})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(x^{2})}^{4}}{x^{2}}$

Multiply the exponents in ${(x^{2})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{2 \cdot 4}}{x^{2}}$

Multiply $2$ by $4$ .

$\frac{x^{8}}{x^{2}}$

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{8}$ .

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

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{2} x^{6}}{x^{2} \cdot 1}$

Cancel the common factor.

$\frac{x^{2} x^{6}}{x^{2} \cdot 1}$

Rewrite the expression.

$\frac{x^{6}}{1}$

Divide $x^{6}$ by $1$ .

$x^{6}$