Finite Math Examples

$(\frac{1}{6}) \cdot {(\frac{5}{6})}^{11}$

Step 1

Apply the product rule to $\frac{5}{6}$ .

$\frac{1}{6} \cdot \frac{5^{11}}{6^{11}}$

Step 2

Combine.

$\frac{1 \cdot 5^{11}}{6 \cdot 6^{11}}$

Step 3

Multiply $6$ by $6^{11}$ by adding the exponents.

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Step 3.1

Multiply $6$ by $6^{11}$ .

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Step 3.1.1

Raise $6$ to the power of $1$ .

$\frac{1 \cdot 5^{11}}{6^{1} \cdot 6^{11}}$

Step 3.1.2

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

$\frac{1 \cdot 5^{11}}{6^{1 + 11}}$

$\frac{1 \cdot 5^{11}}{6^{1 + 11}}$

Step 3.2

Add $1$ and $11$ .

$\frac{1 \cdot 5^{11}}{6^{12}}$

$\frac{1 \cdot 5^{11}}{6^{12}}$

Step 4

Multiply $5^{11}$ by $1$ .

$\frac{5^{11}}{6^{12}}$

Step 5

Raise $5$ to the power of $11$ .

$\frac{48828125}{6^{12}}$

Step 6

Raise $6$ to the power of $12$ .

$\frac{48828125}{2176782336}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{48828125}{2176782336}$

Decimal Form:

$0.02243133 \dots$

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