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

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

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $4$ .

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

Cancel the common factor of $y^{2}$ and $y^{5}$ .

Factor $y^{2}$ out of $2 x^{7} y^{2}$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $5 y^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Apply the product rule to $\frac{2 x^{7}}{5 y^{3}}$ .

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

Apply the product rule to $2 x^{7}$ .

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

Apply the product rule to $5 y^{3}$ .

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

Simplify the numerator.

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

$\frac{8 {(x^{7})}^{3}}{5^{3} {(y^{3})}^{3}}$

Multiply the exponents in ${(x^{7})}^{3}$ .

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

$\frac{8 x^{7 \cdot 3}}{5^{3} {(y^{3})}^{3}}$

Multiply $7$ by $3$ .

$\frac{8 x^{21}}{5^{3} {(y^{3})}^{3}}$

Simplify the denominator.

Raise $5$ to the power of $3$ .

$\frac{8 x^{21}}{125 {(y^{3})}^{3}}$

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

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

$\frac{8 x^{21}}{125 y^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{8 x^{21}}{125 y^{9}}$