Algebra Examples

$81^{- \frac{5}{4}}$

Step 1

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

$\frac{1}{81^{\frac{5}{4}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $81$ as $3^{4}$ .

$\frac{1}{{(3^{4})}^{\frac{5}{4}}}$

Step 2.2

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

$\frac{1}{3^{4 (\frac{5}{4})}}$

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Cancel the common factor.

$\frac{1}{3^{4 (\frac{5}{4})}}$

Step 2.3.2

Rewrite the expression.

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

Step 2.4

Raise $3$ to the power of $5$ .

$\frac{1}{243}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{243}$

Decimal Form:

$0.00411522 \dots$