Algebra Examples

Evaluate

(\frac{1}{27^{\frac{4}{3}}})

$(\frac{1}{27^{\frac{4}{3}}})$

Step 1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

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

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

Step 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{4}{3})}}

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

Step 3

Cancel the common factor of

3

$3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{1}{3^{4}}$

$\frac{1}{3^{4}}$

Step 4

Raise

$3$ to the power of

$4$ .

$\frac{1}{81}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{81}$

Decimal Form:

$0.01234567 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$