Finite Math Examples

${(\frac{1}{6})}^{2} \cdot {(\frac{4}{6})}^{8}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{1}{6}$ .

$\frac{1^{2}}{6^{2}} \cdot {(\frac{4}{6})}^{8}$

Step 1.2

One to any power is one.

$\frac{1}{6^{2}} \cdot {(\frac{4}{6})}^{8}$

Step 1.3

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

$\frac{1}{36} \cdot {(\frac{4}{6})}^{8}$

$\frac{1}{36} \cdot {(\frac{4}{6})}^{8}$

Step 2

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

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Step 2.1

Factor $2$ out of $4$ .

$\frac{1}{36} \cdot {(\frac{2 (2)}{6})}^{8}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6$ .

$\frac{1}{36} \cdot {(\frac{2 \cdot 2}{2 \cdot 3})}^{8}$

Step 2.2.2

Cancel the common factor.

$\frac{1}{36} \cdot {(\frac{2 \cdot 2}{2 \cdot 3})}^{8}$

Step 2.2.3

Rewrite the expression.

$\frac{1}{36} \cdot {(\frac{2}{3})}^{8}$

$\frac{1}{36} \cdot {(\frac{2}{3})}^{8}$

$\frac{1}{36} \cdot {(\frac{2}{3})}^{8}$

Step 3

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

$\frac{1}{36} \cdot \frac{2^{8}}{3^{8}}$

Step 4

Combine.

$\frac{1 \cdot 2^{8}}{36 \cdot 3^{8}}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $2^{8}$ by $1$ .

$\frac{2^{8}}{36 \cdot 3^{8}}$

Step 5.2

Raise $3$ to the power of $8$ .

$\frac{2^{8}}{36 \cdot 6561}$

Step 5.3

Raise $2$ to the power of $8$ .

$\frac{256}{36 \cdot 6561}$

Step 5.4

Multiply $36$ by $6561$ .

$\frac{256}{236196}$

$\frac{256}{236196}$

Step 6

Cancel the common factor of $256$ and $236196$ .

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Step 6.1

Factor $4$ out of $256$ .

$\frac{4 (64)}{236196}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $236196$ .

$\frac{4 \cdot 64}{4 \cdot 59049}$

Step 6.2.2

Cancel the common factor.

$\frac{4 \cdot 64}{4 \cdot 59049}$

Step 6.2.3

Rewrite the expression.

$\frac{64}{59049}$

$\frac{64}{59049}$

$\frac{64}{59049}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{59049}$

Decimal Form:

$0.00108384 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$