Simplify ((4x^2)/(6y^4))^3

${(\frac{4 x^{2}}{6 y^{4}})}^{3}$

Step 1

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 x^{2}$ .

${(\frac{2 (2 x^{2})}{6 y^{4}})}^{3}$

Cancel the common factors.

Factor $2$ out of $6 y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Apply the product rule to $\frac{2 x^{2}}{3 y^{4}}$ .

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

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

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

Apply the product rule to $3 y^{4}$ .

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

Step 3

Simplify the numerator.

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

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

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

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

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

Multiply $2$ by $3$ .

$\frac{8 x^{6}}{3^{3} {(y^{4})}^{3}}$

Step 4

Simplify the denominator.

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

$\frac{8 x^{6}}{27 {(y^{4})}^{3}}$

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

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

$\frac{8 x^{6}}{27 y^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{8 x^{6}}{27 y^{12}}$