Simplify the Radical Expression ((x^4)/(7^-8))^-7

${(\frac{x^{4}}{7^{- 8}})}^{- 7}$

Move $7^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{4} \cdot 7^{8})}^{- 7}$

Raise $7$ to the power of $8$ .

${(x^{4} \cdot 5764801)}^{- 7}$

Move $5764801$ to the left of $x^{4}$ .

${(5764801 \cdot x^{4})}^{- 7}$

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

$\frac{1}{{(5764801 x^{4})}^{7}}$

Simplify the denominator.

Apply the product rule to $5764801 x^{4}$ .

$\frac{1}{5764801^{7} {(x^{4})}^{7}}$

Multiply the exponents in ${(x^{4})}^{7}$ .

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

$\frac{1}{5764801^{7} x^{4 \cdot 7}}$

Multiply $4$ by $7$ .

$\frac{1}{5764801^{7} x^{28}}$