Simplify ((8x^2y^3)/(24x^3y^2))^4

${(\frac{8 x^{2} y^{3}}{24 x^{3} y^{2}})}^{4}$

Step 1

Cancel the common factor of $8$ and $24$ .

Factor $8$ out of $8 x^{2} y^{3}$ .

${(\frac{8 (x^{2} y^{3})}{24 x^{3} y^{2}})}^{4}$

Cancel the common factors.

Factor $8$ out of $24 x^{3} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Factor $x^{2}$ out of $x^{2} y^{3}$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $3 x^{3} y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $y^{3}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{3}$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $3 x y^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

Apply the product rule to $3 x$ .

$\frac{y^{4}}{3^{4} x^{4}}$

Step 5

Raise $3$ to the power of $4$ .

$\frac{y^{4}}{81 x^{4}}$