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

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

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

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

${(- 1)}^{2} {(\frac{5}{x})}^{2} \cdot {(\frac{2 x^{4}}{y^{3}})}^{2}$

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

${(- 1)}^{2} \frac{5^{2}}{x^{2}} \cdot {(\frac{2 x^{4}}{y^{3}})}^{2}$

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{x^{2}} \cdot {(\frac{2 x^{4}}{y^{3}})}^{2}$

Multiply $\frac{5^{2}}{x^{2}}$ by $1$ .

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

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

$\frac{25}{x^{2}} \cdot {(\frac{2 x^{4}}{y^{3}})}^{2}$

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

Apply the product rule to $\frac{2 x^{4}}{y^{3}}$ .

$\frac{25}{x^{2}} \cdot \frac{{(2 x^{4})}^{2}}{{(y^{3})}^{2}}$

Apply the product rule to $2 x^{4}$ .

$\frac{25}{x^{2}} \cdot \frac{2^{2} {(x^{4})}^{2}}{{(y^{3})}^{2}}$

Combine.

$\frac{25 (2^{2} {(x^{4})}^{2})}{x^{2} {(y^{3})}^{2}}$

Simplify the numerator.

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

$\frac{25 \cdot 4 {(x^{4})}^{2}}{x^{2} {(y^{3})}^{2}}$

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

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

$\frac{25 \cdot 4 x^{4 \cdot 2}}{x^{2} {(y^{3})}^{2}}$

Multiply $4$ by $2$ .

$\frac{25 \cdot 4 x^{8}}{x^{2} {(y^{3})}^{2}}$

Multiply $25$ by $4$ .

$\frac{100 x^{8}}{x^{2} {(y^{3})}^{2}}$

Reduce the expression by cancelling the common factors.

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

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

$\frac{100 x^{8}}{x^{2} y^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{100 x^{8}}{x^{2} y^{6}}$

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Factor $x^{2}$ out of $100 x^{8}$ .

$\frac{x^{2} (100 x^{6})}{x^{2} y^{6}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y^{6}$ .

$\frac{x^{2} (100 x^{6})}{x^{2} (y^{6})}$

Cancel the common factor.

$\frac{x^{2} (100 x^{6})}{x^{2} y^{6}}$

Rewrite the expression.

$\frac{100 x^{6}}{y^{6}}$