Simplify (2xy^-5)^3

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

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

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

Multiply $2 x \frac{1}{y^{5}}$ .

Combine $2$ and $\frac{1}{y^{5}}$ .

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

Combine $x$ and $\frac{2}{y^{5}}$ .

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

Move $2$ to the left of $x$ .

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

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

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

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

Apply the product rule to $2 x$ .

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

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

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

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

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

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

Multiply $5$ by $3$ .

$\frac{8 x^{3}}{y^{15}}$