Simplify ((x^5)/(x^7))^2

${(\frac{x^{5}}{x^{7}})}^{2}$

Step 1

Cancel the common factor of $x^{5}$ and $x^{7}$ .

Multiply by $1$ .

${(\frac{x^{5} \cdot 1}{x^{7}})}^{2}$

Cancel the common factors.

Factor $x^{5}$ out of $x^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

${(\frac{1}{x^{2}})}^{2}$

Step 2

Simplify the expression.

Apply the product rule to $\frac{1}{x^{2}}$ .

$\frac{1^{2}}{{(x^{2})}^{2}}$

One to any power is one.

$\frac{1}{{(x^{2})}^{2}}$

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

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

$\frac{1}{x^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{1}{x^{4}}$