Simplify the Radical Expression (64n^12)^(-1/6)

${(64 n^{12})}^{- \frac{1}{6}}$

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

$\frac{1}{{(64 n^{12})}^{\frac{1}{6}}}$

Simplify the denominator.

Apply the product rule to $64 n^{12}$ .

$\frac{1}{64^{\frac{1}{6}} {(n^{12})}^{\frac{1}{6}}}$

Rewrite $64$ as $2^{6}$ .

$\frac{1}{{(2^{6})}^{\frac{1}{6}} {(n^{12})}^{\frac{1}{6}}}$

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

$\frac{1}{2^{6 (\frac{1}{6})} {(n^{12})}^{\frac{1}{6}}}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{1}{2^{6 (\frac{1}{6})} {(n^{12})}^{\frac{1}{6}}}$

Rewrite the expression.

$\frac{1}{2^{1} {(n^{12})}^{\frac{1}{6}}}$

Evaluate the exponent.

$\frac{1}{2 {(n^{12})}^{\frac{1}{6}}}$

Multiply the exponents in ${(n^{12})}^{\frac{1}{6}}$ .

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

$\frac{1}{2 n^{12 (\frac{1}{6})}}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{1}{2 n^{6 (2) \frac{1}{6}}}$

Cancel the common factor.

$\frac{1}{2 n^{6 \cdot 2 \frac{1}{6}}}$

Rewrite the expression.

$\frac{1}{2 n^{2}}$