Simplify ((2y^-4)/(7z^5))^-3

${(\frac{2 y^{- 4}}{7 z^{5}})}^{- 3}$

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2}{7 z^{5} y^{4}})}^{- 3}$

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

${(\frac{7 z^{5} y^{4}}{2})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{7 z^{5} y^{4}}{2}$ .

$\frac{{(7 z^{5} y^{4})}^{3}}{2^{3}}$

Apply the product rule to $7 z^{5} y^{4}$ .

$\frac{{(7 z^{5})}^{3} {(y^{4})}^{3}}{2^{3}}$

Apply the product rule to $7 z^{5}$ .

$\frac{7^{3} {(z^{5})}^{3} {(y^{4})}^{3}}{2^{3}}$

Simplify the numerator.

Raise $7$ to the power of $3$ .

$\frac{343 {(z^{5})}^{3} {(y^{4})}^{3}}{2^{3}}$

Multiply the exponents in ${(z^{5})}^{3}$ .

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

$\frac{343 z^{5 \cdot 3} {(y^{4})}^{3}}{2^{3}}$

Multiply $5$ by $3$ .

$\frac{343 z^{15} {(y^{4})}^{3}}{2^{3}}$

Multiply the exponents in ${(y^{4})}^{3}$ .

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

$\frac{343 z^{15} y^{4 \cdot 3}}{2^{3}}$

Multiply $4$ by $3$ .

$\frac{343 z^{15} y^{12}}{2^{3}}$

Raise $2$ to the power of $3$ .

$\frac{343 z^{15} y^{12}}{8}$