Algebra Examples

$81^{- \frac{1}{2}}$

Step 1

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

$\frac{1}{81^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $81$ as $9^{2}$ .

$\frac{1}{{(9^{2})}^{\frac{1}{2}}}$

Step 2.2

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

$\frac{1}{9^{2 (\frac{1}{2})}}$

Step 2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

$\frac{1}{9^{2 (\frac{1}{2})}}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{9^{1}}$

Step 2.4

Evaluate the exponent.

$\frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$