Find the Product ((3x^2)/(2y^2))^5

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

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

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

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

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

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

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

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

Simplify the numerator.

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

$\frac{243 {(x^{2})}^{5}}{2^{5} {(y^{2})}^{5}}$

Multiply the exponents in ${(x^{2})}^{5}$ .

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

$\frac{243 x^{2 \cdot 5}}{2^{5} {(y^{2})}^{5}}$

Multiply $2$ by $5$ .

$\frac{243 x^{10}}{2^{5} {(y^{2})}^{5}}$

Simplify the denominator.

Raise $2$ to the power of $5$ .

$\frac{243 x^{10}}{32 {(y^{2})}^{5}}$

Multiply the exponents in ${(y^{2})}^{5}$ .

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

$\frac{243 x^{10}}{32 y^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{243 x^{10}}{32 y^{10}}$