Finite Math Examples

$36 \cdot {(\frac{1}{6})}^{2} \cdot {(\frac{5}{6})}^{7}$

Step 1

Simplify the expression.

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Step 1.1

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

$36 \cdot \frac{1^{2}}{6^{2}} \cdot {(\frac{5}{6})}^{7}$

Step 1.2

One to any power is one.

$36 \cdot \frac{1}{6^{2}} \cdot {(\frac{5}{6})}^{7}$

Step 1.3

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

$36 \cdot \frac{1}{36} \cdot {(\frac{5}{6})}^{7}$

Step 2

Cancel the common factor of $36$ .

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Step 2.1

Cancel the common factor.

$36 \cdot \frac{1}{36} \cdot {(\frac{5}{6})}^{7}$

Step 2.2

Rewrite the expression.

$1 \cdot {(\frac{5}{6})}^{7}$

Step 3

Simplify the expression.

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Step 3.1

Multiply ${(\frac{5}{6})}^{7}$ by $1$ .

${(\frac{5}{6})}^{7}$

Step 3.2

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

$\frac{5^{7}}{6^{7}}$

Step 3.3

Raise $5$ to the power of $7$ .

$\frac{78125}{6^{7}}$

Step 3.4

Raise $6$ to the power of $7$ .

$\frac{78125}{279936}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{78125}{279936}$

Decimal Form:

$0.27908164 \dots$