Simplify (-1/(x^2))^2

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

Step 1

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

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

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

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

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

Step 2

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

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

Step 3

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

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

Step 4

One to any power is one.

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

Step 5

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

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

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

Multiply $2$ by $2$ .

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