Simplify ((2x^5y^8)/(5x^6y^5))^2

${(\frac{2 x^{5} y^{8}}{5 x^{6} y^{5}})}^{2}$

Step 1

Cancel the common factor of $x^{5}$ and $x^{6}$ .

Factor $x^{5}$ out of $2 x^{5} y^{8}$ .

${(\frac{x^{5} (2 y^{8})}{5 x^{6} y^{5}})}^{2}$

Cancel the common factors.

Factor $x^{5}$ out of $5 x^{6} y^{5}$ .

${(\frac{x^{5} (2 y^{8})}{x^{5} (5 x y^{5})})}^{2}$

Cancel the common factor.

${(\frac{x^{5} (2 y^{8})}{x^{5} (5 x y^{5})})}^{2}$

Rewrite the expression.

${(\frac{2 y^{8}}{5 x y^{5}})}^{2}$

Step 2

Cancel the common factor of $y^{8}$ and $y^{5}$ .

Factor $y^{5}$ out of $2 y^{8}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Apply the product rule to $\frac{2 y^{3}}{5 x}$ .

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

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

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

Apply the product rule to $5 x$ .

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

Step 4

Simplify the numerator.

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

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

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

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

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

Multiply $3$ by $2$ .

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

Step 5

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

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