Simplify (2x^-2y^4z^-5)^3

${(2 x^{- 2} y^{4} z^{- 5})}^{3}$

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

${(2 \frac{1}{x^{2}} y^{4} z^{- 5})}^{3}$

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

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

Combine $\frac{2}{x^{2}}$ and $y^{4}$ .

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

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

${(\frac{2 y^{4}}{x^{2}} \cdot \frac{1}{z^{5}})}^{3}$

Combine.

${(\frac{2 y^{4} \cdot 1}{x^{2} z^{5}})}^{3}$

Multiply $2$ by $1$ .

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

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

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

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

Apply the product rule to $2 y^{4}$ .

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

Apply the product rule to $x^{2} z^{5}$ .

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

Simplify the numerator.

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

$\frac{8 {(y^{4})}^{3}}{{(x^{2})}^{3} {(z^{5})}^{3}}$

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

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

$\frac{8 y^{4 \cdot 3}}{{(x^{2})}^{3} {(z^{5})}^{3}}$

Multiply $4$ by $3$ .

$\frac{8 y^{12}}{{(x^{2})}^{3} {(z^{5})}^{3}}$

Simplify the denominator.

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\frac{8 y^{12}}{x^{2 \cdot 3} {(z^{5})}^{3}}$

Multiply $2$ by $3$ .

$\frac{8 y^{12}}{x^{6} {(z^{5})}^{3}}$

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

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

$\frac{8 y^{12}}{x^{6} z^{5 \cdot 3}}$

Multiply $5$ by $3$ .

$\frac{8 y^{12}}{x^{6} z^{15}}$