Finite Math Examples

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

Step 1

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

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

Step 2

Combine.

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

Step 3

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

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

Step 4

Multiply $6$ by $6^{5}$ by adding the exponents.

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Step 4.1

Multiply $6$ by $6^{5}$ .

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Step 4.1.1

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

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

Step 4.1.2

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

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

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

Step 4.2

Add $1$ and $5$ .

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

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

Step 5

Evaluate the exponents.

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Step 5.1

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

$6 \cdot \frac{3125}{6^{6}}$

Step 5.2

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

$6 \cdot \frac{3125}{46656}$

$6 \cdot \frac{3125}{46656}$

Step 6

Cancel the common factor of $6$ .

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Step 6.1

Factor $6$ out of $46656$ .

$6 \cdot \frac{3125}{6 (7776)}$

Step 6.2

Cancel the common factor.

$6 \cdot \frac{3125}{6 \cdot 7776}$

Step 6.3

Rewrite the expression.

$\frac{3125}{7776}$

$\frac{3125}{7776}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3125}{7776}$

Decimal Form:

$0.40187757 \dots$

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