Simplify the Radical Expression (4/(64^(5/6)))^(1/2)

${(\frac{4}{64^{\frac{5}{6}}})}^{\frac{1}{2}}$

Step 1

Simplify the denominator.

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

${(\frac{4}{{(2^{6})}^{\frac{5}{6}}})}^{\frac{1}{2}}$

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

${(\frac{4}{2^{6 (\frac{5}{6})}})}^{\frac{1}{2}}$

Cancel the common factor of $6$ .

Cancel the common factor.

${(\frac{4}{2^{6 (\frac{5}{6})}})}^{\frac{1}{2}}$

Rewrite the expression.

${(\frac{4}{2^{5}})}^{\frac{1}{2}}$

Raise $2$ to the power of $5$ .

${(\frac{4}{32})}^{\frac{1}{2}}$

Step 2

Cancel the common factor of $4$ and $32$ .

Factor $4$ out of $4$ .

${(\frac{4 (1)}{32})}^{\frac{1}{2}}$

Cancel the common factors.

Factor $4$ out of $32$ .

${(\frac{4 \cdot 1}{4 \cdot 8})}^{\frac{1}{2}}$

Cancel the common factor.

${(\frac{4 \cdot 1}{4 \cdot 8})}^{\frac{1}{2}}$

Rewrite the expression.

${(\frac{1}{8})}^{\frac{1}{2}}$

Step 3

Apply the product rule to $\frac{1}{8}$ .

$\frac{1^{\frac{1}{2}}}{8^{\frac{1}{2}}}$

Step 4

One to any power is one.

$\frac{1}{8^{\frac{1}{2}}}$