Basic Math Examples

$\frac{{(\frac{2}{3})}^{10}}{{(\frac{2}{3})}^{21}}$

Step 1

Cancel the common factor of ${(\frac{2}{3})}^{10}$ and ${(\frac{2}{3})}^{21}$ .

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Step 1.1

Multiply by $1$ .

$\frac{{(\frac{2}{3})}^{10} \cdot 1}{{(\frac{2}{3})}^{21}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor ${(\frac{2}{3})}^{10}$ out of ${(\frac{2}{3})}^{21}$ .

$\frac{{(\frac{2}{3})}^{10} \cdot 1}{{(\frac{2}{3})}^{10} {(\frac{2}{3})}^{11}}$

Step 1.2.2

Cancel the common factor.

$\frac{{(\frac{2}{3})}^{10} \cdot 1}{{(\frac{2}{3})}^{10} {(\frac{2}{3})}^{11}}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{{(\frac{2}{3})}^{11}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{1}{\frac{2^{11}}{3^{11}}}$

Step 2.2

Raise $2$ to the power of $11$ .

$\frac{1}{\frac{2048}{3^{11}}}$

Step 2.3

Raise $3$ to the power of $11$ .

$\frac{1}{\frac{2048}{177147}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{177147}{2048})$

Step 4

Multiply $\frac{177147}{2048}$ by $1$ .

$\frac{177147}{2048}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{177147}{2048}$

Decimal Form:

$86.49755859 \dots$

Mixed Number Form:

$86 \frac{1019}{2048}$