Evaluate (64)^(-4/3)

${(64)}^{- \frac{4}{3}}$

Step 1

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

$\frac{1}{64^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

Rewrite $64$ as $4^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4^{4}}$

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

$\frac{1}{256}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{256}$

Decimal Form:

$0.00390625$