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

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

Step 1

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

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

Step 2

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

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

Step 3

Combine $\frac{2}{x^{5}}$ and $y^{4}$ .

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

Step 4

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

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

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

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

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

Step 5

Simplify the numerator.

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

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

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

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

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

Multiply $4$ by $3$ .

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

Step 6

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

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

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

Multiply $5$ by $3$ .

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