Evaluate (4x^3)(2x)^-4

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

Step 1

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

$4 x^{3} \frac{1}{{(2 x)}^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 x$ .

$4 x^{3} \frac{1}{2^{4} x^{4}}$

Raise $2$ to the power of $4$ .

$4 x^{3} \frac{1}{16 x^{4}}$

Step 3

Cancel the common factor of $4 x^{3}$ .

Factor $4 x^{3}$ out of $16 x^{4}$ .

$4 x^{3} \frac{1}{4 x^{3} (4 x)}$

Cancel the common factor.

$4 x^{3} \frac{1}{4 x^{3} (4 x)}$

Rewrite the expression.

$\frac{1}{4 x}$