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

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

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

Factor $x^{2}$ out of $3 x^{5}$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $5 x^{2} y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Apply the product rule to $\frac{3 x^{3}}{5 y^{4}}$ .

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

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

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

Apply the product rule to $5 y^{4}$ .

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

Step 4

Simplify the numerator.

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

$\frac{9 {(x^{3})}^{2}}{5^{2} {(y^{4})}^{2}}$

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

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

$\frac{9 x^{3 \cdot 2}}{5^{2} {(y^{4})}^{2}}$

Multiply $3$ by $2$ .

$\frac{9 x^{6}}{5^{2} {(y^{4})}^{2}}$

Step 5

Simplify the denominator.

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

$\frac{9 x^{6}}{25 {(y^{4})}^{2}}$

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

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

$\frac{9 x^{6}}{25 y^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{9 x^{6}}{25 y^{8}}$