Evaluate 512^(-5/3)

$512^{- \frac{5}{3}}$

Step 1

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

$\frac{1}{512^{\frac{5}{3}}}$

Step 2

Simplify the denominator.

Rewrite $512$ as $8^{3}$ .

$\frac{1}{{(8^{3})}^{\frac{5}{3}}}$

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

$\frac{1}{8^{3 (\frac{5}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{8^{3 (\frac{5}{3})}}$

Rewrite the expression.

$\frac{1}{8^{5}}$

Raise $8$ to the power of $5$ .

$\frac{1}{32768}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{32768}$

Decimal Form:

$3.05175781 \cdot 10^{- 5}$