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

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

Step 1

Move ${(x^{2})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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

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

Multiply $2$ by $2$ .

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

Step 3

Multiply $x$ by $x^{4}$ by adding the exponents.

Multiply $x$ by $x^{4}$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $4$ .

$\frac{1}{x^{5}}$