Evaluate ((16x^-4)^2)/((4x^-2)^3)

$\frac{{(16 x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Simplify the numerator.

Apply the product rule to $16 x^{- 4}$ .

$\frac{16^{2} {(x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Raise $16$ to the power of $2$ .

$\frac{256 {(x^{- 4})}^{2}}{{(4 x^{- 2})}^{3}}$

Multiply the exponents in ${(x^{- 4})}^{2}$ .

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

$\frac{256 x^{- 4 \cdot 2}}{{(4 x^{- 2})}^{3}}$

Multiply $- 4$ by $2$ .

$\frac{256 x^{- 8}}{{(4 x^{- 2})}^{3}}$

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

$\frac{256 \frac{1}{x^{8}}}{{(4 x^{- 2})}^{3}}$

Simplify the denominator.

Apply the product rule to $4 x^{- 2}$ .

$\frac{256 \frac{1}{x^{8}}}{4^{3} {(x^{- 2})}^{3}}$

Raise $4$ to the power of $3$ .

$\frac{256 \frac{1}{x^{8}}}{64 {(x^{- 2})}^{3}}$

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

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

$\frac{256 \frac{1}{x^{8}}}{64 x^{- 2 \cdot 3}}$

Multiply $- 2$ by $3$ .

$\frac{256 \frac{1}{x^{8}}}{64 x^{- 6}}$

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

$\frac{256 \frac{1}{x^{8}}}{64 \frac{1}{x^{6}}}$

Combine fractions.

Combine $256$ and $\frac{1}{x^{8}}$ .

$\frac{\frac{256}{x^{8}}}{64 \frac{1}{x^{6}}}$

Combine $64$ and $\frac{1}{x^{6}}$ .

$\frac{\frac{256}{x^{8}}}{\frac{64}{x^{6}}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{256}{x^{8}} \cdot \frac{x^{6}}{64}$

Combine.

$\frac{256 x^{6}}{x^{8} \cdot 64}$

Cancel the common factor of $256$ and $64$ .

Factor $64$ out of $256 x^{6}$ .

$\frac{64 (4 x^{6})}{x^{8} \cdot 64}$

Cancel the common factors.

Factor $64$ out of $x^{8} \cdot 64$ .

$\frac{64 (4 x^{6})}{64 \cdot x^{8}}$

Cancel the common factor.

$\frac{64 (4 x^{6})}{64 \cdot x^{8}}$

Rewrite the expression.

$\frac{4 x^{6}}{x^{8}}$

Cancel the common factor of $x^{6}$ and $x^{8}$ .

Factor $x^{6}$ out of $4 x^{6}$ .

$\frac{x^{6} \cdot 4}{x^{8}}$

Cancel the common factors.

Factor $x^{6}$ out of $x^{8}$ .

$\frac{x^{6} \cdot 4}{x^{6} x^{2}}$

Cancel the common factor.

$\frac{x^{6} \cdot 4}{x^{6} x^{2}}$

Rewrite the expression.

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

Evaluate ((16x^-4)^2)/((4x^-2)^3)

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