Finite Math Examples

$495 {(\frac{1}{6})}^{4} {(\frac{5}{6})}^{8}$

Step 1

Simplify the expression.

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Step 1.1

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

$495 \frac{1^{4}}{6^{4}} {(\frac{5}{6})}^{8}$

Step 1.2

One to any power is one.

$495 \frac{1}{6^{4}} {(\frac{5}{6})}^{8}$

Step 1.3

Raise $6$ to the power of $4$ .

$495 (\frac{1}{1296}) {(\frac{5}{6})}^{8}$

$495 (\frac{1}{1296}) {(\frac{5}{6})}^{8}$

Step 2

Cancel the common factor of $9$ .

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Step 2.1

Factor $9$ out of $495$ .

$9 (55) \frac{1}{1296} {(\frac{5}{6})}^{8}$

Step 2.2

Factor $9$ out of $1296$ .

$9 \cdot 55 \frac{1}{9 \cdot 144} {(\frac{5}{6})}^{8}$

Step 2.3

Cancel the common factor.

$9 \cdot 55 \frac{1}{9 \cdot 144} {(\frac{5}{6})}^{8}$

Step 2.4

Rewrite the expression.

$55 (\frac{1}{144}) {(\frac{5}{6})}^{8}$

$55 (\frac{1}{144}) {(\frac{5}{6})}^{8}$

Step 3

Combine $55$ and $\frac{1}{144}$ .

$\frac{55}{144} {(\frac{5}{6})}^{8}$

Step 4

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

$\frac{55}{144} \cdot \frac{5^{8}}{6^{8}}$

Step 5

Combine.

$\frac{55 \cdot 5^{8}}{144 \cdot 6^{8}}$

Step 6

Simplify the expression.

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Step 6.1

Raise $5$ to the power of $8$ .

$\frac{55 \cdot 390625}{144 \cdot 6^{8}}$

Step 6.2

Raise $6$ to the power of $8$ .

$\frac{55 \cdot 390625}{144 \cdot 1679616}$

Step 6.3

Multiply $55$ by $390625$ .

$\frac{21484375}{144 \cdot 1679616}$

Step 6.4

Multiply $144$ by $1679616$ .

$\frac{21484375}{241864704}$

$\frac{21484375}{241864704}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{21484375}{241864704}$

Decimal Form:

$0.08882807 \dots$

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