Simplify ((5x)/y)^2((y^3)/(10x^2))

${(\frac{5 x}{y})}^{2} (\frac{y^{3}}{10 x^{2}})$

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

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

$\frac{{(5 x)}^{2}}{y^{2}} \cdot \frac{y^{3}}{10 x^{2}}$

Apply the product rule to $5 x$ .

$\frac{5^{2} x^{2}}{y^{2}} \cdot \frac{y^{3}}{10 x^{2}}$

Combine.

$\frac{5^{2} x^{2} y^{3}}{y^{2} (10 x^{2})}$

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

Cancel the common factor.

$\frac{5^{2} x^{2} y^{3}}{y^{2} (10 x^{2})}$

Rewrite the expression.

$\frac{5^{2} y^{3}}{y^{2} \cdot (10)}$

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

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

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

Cancel the common factors.

Factor $y^{2}$ out of $y^{2} \cdot (10)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5^{2} y}{10}$

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

$\frac{25 y}{10}$

Cancel the common factor of $25$ and $10$ .

Factor $5$ out of $25 y$ .

$\frac{5 (5 y)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (5 y)}{5 (2)}$

Cancel the common factor.

$\frac{5 (5 y)}{5 \cdot 2}$

Rewrite the expression.

$\frac{5 y}{2}$