Simplify ((3x^5y^3)/(x^3y^6))^4

${(\frac{3 x^{5} y^{3}}{x^{3} y^{6}})}^{4}$

Step 1

Cancel the common factor of $x^{5}$ and $x^{3}$ .

Factor $x^{3}$ out of $3 x^{5} y^{3}$ .

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

Cancel the common factors.

Factor $x^{3}$ out of $x^{3} y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $y^{3}$ and $y^{6}$ .

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

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

Cancel the common factors.

Factor $y^{3}$ out of $y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

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

Apply the product rule to $3 x^{2}$ .

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

Step 4

Simplify the numerator.

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

$\frac{81 {(x^{2})}^{4}}{{(y^{3})}^{4}}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$\frac{81 x^{2 \cdot 4}}{{(y^{3})}^{4}}$

Multiply $2$ by $4$ .

$\frac{81 x^{8}}{{(y^{3})}^{4}}$

Step 5

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

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

$\frac{81 x^{8}}{y^{3 \cdot 4}}$

Multiply $3$ by $4$ .

$\frac{81 x^{8}}{y^{12}}$