Simplify (3x^-4)^-4

${(3 x^{- 4})}^{- 4}$

Step 1

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

${(3 \frac{1}{x^{4}})}^{- 4}$

Step 2

Combine $3$ and $\frac{1}{x^{4}}$ .

${(\frac{3}{x^{4}})}^{- 4}$

Step 3

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

${(\frac{x^{4}}{3})}^{4}$

Step 4

Apply the product rule to $\frac{x^{4}}{3}$ .

$\frac{{(x^{4})}^{4}}{3^{4}}$

Step 5

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

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

$\frac{x^{4 \cdot 4}}{3^{4}}$

Multiply $4$ by $4$ .

$\frac{x^{16}}{3^{4}}$

Step 6

Raise $3$ to the power of $4$ .

$\frac{x^{16}}{81}$