Finite Math Examples

$66 {(\frac{1}{3})}^{10} {(\frac{2}{3})}^{2}$

Step 1

Simplify terms.

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Step 1.1

Apply the product rule to $\frac{1}{3}$ .

$66 \frac{1^{10}}{3^{10}} {(\frac{2}{3})}^{2}$

Step 1.2

Simplify the expression.

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Step 1.2.1

One to any power is one.

$66 \frac{1}{3^{10}} {(\frac{2}{3})}^{2}$

Step 1.2.2

Raise $3$ to the power of $10$ .

$66 (\frac{1}{59049}) {(\frac{2}{3})}^{2}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $66$ .

$3 (22) \frac{1}{59049} {(\frac{2}{3})}^{2}$

Step 1.3.2

Factor $3$ out of $59049$ .

$3 \cdot 22 \frac{1}{3 \cdot 19683} {(\frac{2}{3})}^{2}$

Step 1.3.3

Cancel the common factor.

$3 \cdot 22 \frac{1}{3 \cdot 19683} {(\frac{2}{3})}^{2}$

Step 1.3.4

Rewrite the expression.

$22 (\frac{1}{19683}) {(\frac{2}{3})}^{2}$

Step 1.4

Combine $22$ and $\frac{1}{19683}$ .

$\frac{22}{19683} {(\frac{2}{3})}^{2}$

Step 1.5

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

$\frac{22}{19683} \cdot \frac{2^{2}}{3^{2}}$

Step 1.6

Combine.

$\frac{22 \cdot 2^{2}}{19683 \cdot 3^{2}}$

Step 1.7

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

$\frac{22 \cdot 4}{19683 \cdot 3^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $19683$ as $3^{9}$ .

$\frac{22 \cdot 4}{3^{9} \cdot 3^{2}}$

Step 2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{22 \cdot 4}{3^{9 + 2}}$

Step 2.3

Add $9$ and $2$ .

$\frac{22 \cdot 4}{3^{11}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $22$ by $4$ .

$\frac{88}{3^{11}}$

Step 3.2

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

$\frac{88}{177147}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{88}{177147}$

Decimal Form:

$0.00049676 \dots$