Evaluate 216^(-5/3)

$216^{- \frac{5}{3}}$

Step 1

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

$\frac{1}{216^{\frac{5}{3}}}$

Step 2

Simplify the denominator.

Rewrite $216$ as $6^{3}$ .

$\frac{1}{{(6^{3})}^{\frac{5}{3}}}$

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

$\frac{1}{6^{3 (\frac{5}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{6^{3 (\frac{5}{3})}}$

Rewrite the expression.

$\frac{1}{6^{5}}$

Raise $6$ to the power of $5$ .

$\frac{1}{7776}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7776}$

Decimal Form:

$0.00012860 \dots$