Basic Math Examples

{| {({(\frac{2}{3})}^{2})}^{3} |}^{- 4}

${| {({(\frac{2}{3})}^{2})}^{3} |}^{- 4}$

Step 1

Multiply the exponents in

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

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

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Step 1.1

Apply the power rule and multiply exponents,

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

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

{| {(\frac{2}{3})}^{2 \cdot 3} |}^{- 4}

${| {(\frac{2}{3})}^{2 \cdot 3} |}^{- 4}$

Step 1.2

Multiply

2

$2$ by

3

$3$ .

{| {(\frac{2}{3})}^{6} |}^{- 4}

${| {(\frac{2}{3})}^{6} |}^{- 4}$

{| {(\frac{2}{3})}^{6} |}^{- 4}

${| {(\frac{2}{3})}^{6} |}^{- 4}$

Step 2

Apply the product rule to

\frac{2}{3}

$\frac{2}{3}$ .

{| \frac{2^{6}}{3^{6}} |}^{- 4}

${| \frac{2^{6}}{3^{6}} |}^{- 4}$

Step 3

Raise

2

$2$ to the power of

6

$6$ .

{| \frac{64}{3^{6}} |}^{- 4}

${| \frac{64}{3^{6}} |}^{- 4}$

Step 4

Raise

3

$3$ to the power of

6

$6$ .

{| \frac{64}{729} |}^{- 4}

${| \frac{64}{729} |}^{- 4}$

Step 5

\frac{64}{729}

$\frac{64}{729}$ is approximately

0.08779149

$0.08779149$ which is positive so remove the absolute value

{(\frac{64}{729})}^{- 4}

${(\frac{64}{729})}^{- 4}$

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

{(\frac{729}{64})}^{4}

${(\frac{729}{64})}^{4}$

Step 7

Apply the product rule to

\frac{729}{64}

$\frac{729}{64}$ .

\frac{729^{4}}{64^{4}}

$\frac{729^{4}}{64^{4}}$

Step 8

Raise

729

$729$ to the power of

4

$4$ .

\frac{282429536481}{64^{4}}

$\frac{282429536481}{64^{4}}$

Step 9

Raise

64

$64$ to the power of

4

$4$ .

\frac{282429536481}{16777216}

$\frac{282429536481}{16777216}$

Step 10

The result can be shown in multiple forms.

Exact Form:

\frac{282429536481}{16777216}

$\frac{282429536481}{16777216}$

Decimal Form:

16834.11219602 \dots

$16834.11219602 \dots$

Mixed Number Form:

16834 \frac{1882337}{16777216}

$16834 \frac{1882337}{16777216}$