Simplify ((2x)^-2)/((2x^3)^-1)

$\frac{{(2 x)}^{- 2}}{{(2 x^{3})}^{- 1}}$

Step 1

Simplify the expression.

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

$\frac{1}{{(2 x^{3})}^{- 1} {(2 x)}^{2}}$

Move ${(2 x^{3})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the denominator.

Apply the product rule to $2 x$ .

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

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

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{2}$