Finite Math Examples

$10 (\frac{1}{6}) \cdot {(\frac{4}{6})}^{9}$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $10$ .

$2 (5) \frac{1}{6} \cdot {(\frac{4}{6})}^{9}$

Step 1.2

Factor $2$ out of $6$ .

$2 \cdot 5 \frac{1}{2 \cdot 3} \cdot {(\frac{4}{6})}^{9}$

Step 1.3

Cancel the common factor.

$2 \cdot 5 \frac{1}{2 \cdot 3} \cdot {(\frac{4}{6})}^{9}$

Step 1.4

Rewrite the expression.

$5 (\frac{1}{3}) \cdot {(\frac{4}{6})}^{9}$

Step 2

Combine $5$ and $\frac{1}{3}$ .

$\frac{5}{3} \cdot {(\frac{4}{6})}^{9}$

Step 3

Cancel the common factor of $4$ and $6$ .

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Step 3.1

Factor $2$ out of $4$ .

$\frac{5}{3} \cdot {(\frac{2 (2)}{6})}^{9}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

$\frac{5}{3} \cdot {(\frac{2 \cdot 2}{2 \cdot 3})}^{9}$

Step 3.2.2

Cancel the common factor.

$\frac{5}{3} \cdot {(\frac{2 \cdot 2}{2 \cdot 3})}^{9}$

Step 3.2.3

Rewrite the expression.

$\frac{5}{3} \cdot {(\frac{2}{3})}^{9}$

Step 4

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

$\frac{5}{3} \cdot \frac{2^{9}}{3^{9}}$

Step 5

Combine.

$\frac{5 \cdot 2^{9}}{3 \cdot 3^{9}}$

Step 6

Multiply $3$ by $3^{9}$ by adding the exponents.

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Step 6.1

Multiply $3$ by $3^{9}$ .

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Step 6.1.1

Raise $3$ to the power of $1$ .

$\frac{5 \cdot 2^{9}}{3^{1} \cdot 3^{9}}$

Step 6.1.2

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

$\frac{5 \cdot 2^{9}}{3^{1 + 9}}$

Step 6.2

Add $1$ and $9$ .

$\frac{5 \cdot 2^{9}}{3^{10}}$

Step 7

Raise $2$ to the power of $9$ .

$\frac{5 \cdot 512}{3^{10}}$

Step 8

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

$\frac{5 \cdot 512}{59049}$

Step 9

Multiply $5$ by $512$ .

$\frac{2560}{59049}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{2560}{59049}$

Decimal Form:

$0.04335382 \dots$