Finite Math Examples

$15 {(\frac{1}{6})}^{2} {(\frac{5}{6})}^{4}$

Step 1

Simplify the expression.

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Step 1.1

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

$15 \frac{1^{2}}{6^{2}} {(\frac{5}{6})}^{4}$

Step 1.2

One to any power is one.

$15 \frac{1}{6^{2}} {(\frac{5}{6})}^{4}$

Step 1.3

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

$15 (\frac{1}{36}) {(\frac{5}{6})}^{4}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Factor $3$ out of $15$ .

$3 (5) \frac{1}{36} {(\frac{5}{6})}^{4}$

Step 2.2

Factor $3$ out of $36$ .

$3 \cdot 5 \frac{1}{3 \cdot 12} {(\frac{5}{6})}^{4}$

Step 2.3

Cancel the common factor.

$3 \cdot 5 \frac{1}{3 \cdot 12} {(\frac{5}{6})}^{4}$

Step 2.4

Rewrite the expression.

$5 (\frac{1}{12}) {(\frac{5}{6})}^{4}$

Step 3

Combine $5$ and $\frac{1}{12}$ .

$\frac{5}{12} {(\frac{5}{6})}^{4}$

Step 4

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

$\frac{5}{12} \cdot \frac{5^{4}}{6^{4}}$

Step 5

Combine.

$\frac{5 \cdot 5^{4}}{12 \cdot 6^{4}}$

Step 6

Multiply $5$ by $5^{4}$ by adding the exponents.

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Step 6.1

Multiply $5$ by $5^{4}$ .

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Step 6.1.1

Raise $5$ to the power of $1$ .

$\frac{5^{1} \cdot 5^{4}}{12 \cdot 6^{4}}$

Step 6.1.2

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

$\frac{5^{1 + 4}}{12 \cdot 6^{4}}$

Step 6.2

Add $1$ and $4$ .

$\frac{5^{5}}{12 \cdot 6^{4}}$

Step 7

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

$\frac{3125}{12 \cdot 6^{4}}$

Step 8

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

$\frac{3125}{12 \cdot 1296}$

Step 9

Multiply $12$ by $1296$ .

$\frac{3125}{15552}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{3125}{15552}$

Decimal Form:

$0.20093878 \dots$