Simplify the Radical Expression (1/64)^(1/6)

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

Apply the product rule to $\frac{1}{64}$ .

$\frac{1^{\frac{1}{6}}}{64^{\frac{1}{6}}}$

One to any power is one.

$\frac{1}{64^{\frac{1}{6}}}$

Simplify the denominator.

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

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

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

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{2}$