Simplify ((5x^6y^2)/(10x^4y))^2

${(\frac{5 x^{6} y^{2}}{10 x^{4} y})}^{2}$

Step 1

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5 x^{6} y^{2}$ .

${(\frac{5 (x^{6} y^{2})}{10 x^{4} y})}^{2}$

Cancel the common factors.

Factor $5$ out of $10 x^{4} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $x^{6} y^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

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

Cancel the common factors.

Factor $y$ out of $2 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

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

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

Step 5

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

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

$\frac{x^{2 \cdot 2} y^{2}}{2^{2}}$

Multiply $2$ by $2$ .

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

Step 6

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

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

Simplify ((5x^6y^2)/(10x^4y))^2

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