Algebra Examples

27^{- \frac{2}{3}}

$27^{- \frac{2}{3}}$

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{27^{\frac{2}{3}}}

$\frac{1}{27^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

\frac{1}{{(3^{3})}^{\frac{2}{3}}}

$\frac{1}{{(3^{3})}^{\frac{2}{3}}}$

Step 2.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{1}{3^{3 (\frac{2}{3})}}

$\frac{1}{3^{3 (\frac{2}{3})}}$

Step 2.3

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 2.3.1

Cancel the common factor.

\frac{1}{3^{3 (\frac{2}{3})}}

$\frac{1}{3^{3 (\frac{2}{3})}}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{3^{2}}$

Step 2.4

Raise

$3$ to the power of

$2$ .

$\frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$