Simplify ((4x^7)/(6x))^2

${(\frac{4 x^{7}}{6 x})}^{2}$

Step 1

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 x^{7}$ .

${(\frac{2 (2 x^{7})}{6 x})}^{2}$

Cancel the common factors.

Factor $2$ out of $6 x$ .

${(\frac{2 (2 x^{7})}{2 (3 x)})}^{2}$

Cancel the common factor.

${(\frac{2 (2 x^{7})}{2 (3 x)})}^{2}$

Rewrite the expression.

${(\frac{2 x^{7}}{3 x})}^{2}$

Step 2

Cancel the common factor of $x^{7}$ and $x$ .

Factor $x$ out of $2 x^{7}$ .

${(\frac{x (2 x^{6})}{3 x})}^{2}$

Cancel the common factors.

Factor $x$ out of $3 x$ .

${(\frac{x (2 x^{6})}{x \cdot 3})}^{2}$

Cancel the common factor.

${(\frac{x (2 x^{6})}{x \cdot 3})}^{2}$

Rewrite the expression.

${(\frac{2 x^{6}}{3})}^{2}$

Step 3

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

Apply the product rule to $\frac{2 x^{6}}{3}$ .

$\frac{{(2 x^{6})}^{2}}{3^{2}}$

Apply the product rule to $2 x^{6}$ .

$\frac{2^{2} {(x^{6})}^{2}}{3^{2}}$

Step 4

Simplify the numerator.

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

$\frac{4 {(x^{6})}^{2}}{3^{2}}$

Multiply the exponents in ${(x^{6})}^{2}$ .

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

$\frac{4 x^{6 \cdot 2}}{3^{2}}$

Multiply $6$ by $2$ .

$\frac{4 x^{12}}{3^{2}}$

Step 5

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

$\frac{4 x^{12}}{9}$