Simplify ((2x^-3)^2)/(4x^4)

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

Simplify the numerator.

Apply the product rule to $2 x^{- 3}$ .

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

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

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

Multiply the exponents in ${(x^{- 3})}^{2}$ .

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

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

Multiply $- 3$ by $2$ .

$\frac{4 x^{- 6}}{4 x^{4}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 \frac{1}{x^{6}}}{4 x^{4}}$

Combine $4$ and $\frac{1}{x^{6}}$ .

$\frac{\frac{4}{x^{6}}}{4 x^{4}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{x^{6}} \cdot \frac{1}{4 x^{4}}$

Combine.

$\frac{4 \cdot 1}{x^{6} (4 x^{4})}$

Multiply $x^{6}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{4 \cdot 1}{x^{4} x^{6} \cdot 4}$

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

$\frac{4 \cdot 1}{x^{4 + 6} \cdot 4}$

Add $4$ and $6$ .

$\frac{4 \cdot 1}{x^{10} \cdot 4}$

Multiply $4$ by $1$ .

$\frac{4}{x^{10} \cdot 4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{x^{10} \cdot 4}$

Rewrite the expression.

$\frac{1}{x^{10}}$