Finite Math Examples

$10 \cdot {(\frac{1}{6})}^{3} \cdot {(\frac{5}{6})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

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

$10 \cdot \frac{1^{3}}{6^{3}} \cdot {(\frac{5}{6})}^{2}$

Step 1.2

One to any power is one.

$10 \cdot \frac{1}{6^{3}} \cdot {(\frac{5}{6})}^{2}$

Step 1.3

Raise $6$ to the power of $3$ .

$10 \cdot \frac{1}{216} \cdot {(\frac{5}{6})}^{2}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $10$ .

$2 (5) \cdot \frac{1}{216} \cdot {(\frac{5}{6})}^{2}$

Step 2.2

Factor $2$ out of $216$ .

$2 \cdot 5 \cdot \frac{1}{2 \cdot 108} \cdot {(\frac{5}{6})}^{2}$

Step 2.3

Cancel the common factor.

$2 \cdot 5 \cdot \frac{1}{2 \cdot 108} \cdot {(\frac{5}{6})}^{2}$

Step 2.4

Rewrite the expression.

$5 \cdot \frac{1}{108} \cdot {(\frac{5}{6})}^{2}$

Step 3

Combine $5$ and $\frac{1}{108}$ .

$\frac{5}{108} \cdot {(\frac{5}{6})}^{2}$

Step 4

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

$\frac{5}{108} \cdot \frac{5^{2}}{6^{2}}$

Step 5

Combine.

$\frac{5 \cdot 5^{2}}{108 \cdot 6^{2}}$

Step 6

Multiply $5$ by $5^{2}$ by adding the exponents.

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Step 6.1

Multiply $5$ by $5^{2}$ .

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Step 6.1.1

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

$\frac{5^{1} \cdot 5^{2}}{108 \cdot 6^{2}}$

Step 6.1.2

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

$\frac{5^{1 + 2}}{108 \cdot 6^{2}}$

Step 6.2

Add $1$ and $2$ .

$\frac{5^{3}}{108 \cdot 6^{2}}$

Step 7

Raise $5$ to the power of $3$ .

$\frac{125}{108 \cdot 6^{2}}$

Step 8

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

$\frac{125}{108 \cdot 36}$

Step 9

Multiply $108$ by $36$ .

$\frac{125}{3888}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{125}{3888}$

Decimal Form:

$0.03215020 \dots$