Evaluate (2x^-6)^-2

${(2 x^{- 6})}^{- 2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(2 \frac{1}{x^{6}})}^{- 2}$

Step 2

Combine $2$ and $\frac{1}{x^{6}}$ .

${(\frac{2}{x^{6}})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

Apply the product rule to $\frac{x^{6}}{2}$ .

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

Step 5

Multiply the exponents in ${(x^{6})}^{2}$ .

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

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

Multiply $6$ by $2$ .

$\frac{x^{12}}{2^{2}}$

Step 6

Raise $2$ to the power of $2$ .

$\frac{x^{12}}{4}$