Algebra Examples

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

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.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

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:

$0.00012860 \dots$