Basic Math Examples

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

Step 1

Multiply the exponents in ${({(\frac{2}{3})}^{2})}^{3}$ .

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Step 1.1

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

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

Step 1.2

Multiply $2$ by $3$ .

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

Step 2

Apply the product rule to $\frac{2}{3}$ .

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

Step 3

Raise $2$ to the power of $6$ .

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

Step 4

Raise $3$ to the power of $6$ .

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

Step 5

$\frac{64}{729}$ is approximately $0.08779149$ which is positive so remove the absolute value

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

Step 6

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

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

Step 7

Apply the product rule to $\frac{729}{64}$ .

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

Step 8

Raise $729$ to the power of $4$ .

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

Step 9

Raise $64$ to the power of $4$ .

$\frac{282429536481}{16777216}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{282429536481}{16777216}$

Decimal Form:

$16834.11219602 \dots$

Mixed Number Form:

$16834 \frac{1882337}{16777216}$