Finite Math Examples

$119759850 \cdot {(\frac{2}{30})}^{13} \cdot {(\frac{14}{15})}^{7}$

Step 1

Cancel the common factor of $2$ and $30$ .

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Step 1.1

Factor $2$ out of $2$ .

$119759850 \cdot {(\frac{2 (1)}{30})}^{13} \cdot {(\frac{14}{15})}^{7}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $30$ .

$119759850 \cdot {(\frac{2 \cdot 1}{2 \cdot 15})}^{13} \cdot {(\frac{14}{15})}^{7}$

Step 1.2.2

Cancel the common factor.

$119759850 \cdot {(\frac{2 \cdot 1}{2 \cdot 15})}^{13} \cdot {(\frac{14}{15})}^{7}$

Step 1.2.3

Rewrite the expression.

$119759850 \cdot {(\frac{1}{15})}^{13} \cdot {(\frac{14}{15})}^{7}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{1}{15}$ .

$119759850 \cdot \frac{1^{13}}{15^{13}} \cdot {(\frac{14}{15})}^{7}$

Step 2.2

One to any power is one.

$119759850 \cdot \frac{1}{15^{13}} \cdot {(\frac{14}{15})}^{7}$

Step 2.3

Raise $15$ to the power of $13$ .

$119759850 \cdot \frac{1}{1946195068359380} \cdot {(\frac{14}{15})}^{7}$

Step 3

Cancel the common factor of $10$ .

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Step 3.1

Factor $10$ out of $119759850$ .

$10 (11975985) \cdot \frac{1}{1946195068359380} \cdot {(\frac{14}{15})}^{7}$

Step 3.2

Factor $10$ out of $1946195068359380$ .

$10 \cdot 11975985 \cdot \frac{1}{10 \cdot 194619506835938} \cdot {(\frac{14}{15})}^{7}$

Step 3.3

Cancel the common factor.

$10 \cdot 11975985 \cdot \frac{1}{10 \cdot 194619506835938} \cdot {(\frac{14}{15})}^{7}$

Step 3.4

Rewrite the expression.

$11975985 \cdot \frac{1}{194619506835938} \cdot {(\frac{14}{15})}^{7}$

Step 4

Combine $11975985$ and $\frac{1}{194619506835938}$ .

$\frac{11975985}{194619506835938} \cdot {(\frac{14}{15})}^{7}$

Step 5

Apply the product rule to $\frac{14}{15}$ .

$\frac{11975985}{194619506835938} \cdot \frac{14^{7}}{15^{7}}$

Step 6

Combine.

$\frac{11975985 \cdot 14^{7}}{194619506835938 \cdot 15^{7}}$

Step 7

Simplify the expression.

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Step 7.1

Raise $14$ to the power of $7$ .

$\frac{11975985 \cdot 105413504}{194619506835938 \cdot 15^{7}}$

Step 7.2

Raise $15$ to the power of $7$ .

$\frac{11975985 \cdot 105413504}{194619506835938 \cdot 170859375}$

Step 7.3

Multiply $11975985$ by $105413504$ .

$\frac{1262430542701440}{194619506835938 \cdot 170859375}$

Step 7.4

Multiply $194619506835938$ by $170859375$ .

$\frac{1262430542701440}{33252567300796594218750}$

Step 8

Cancel the common factor of $1262430542701440$ and $33252567300796594218750$ .

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Step 8.1

Factor $270$ out of $1262430542701440$ .

$\frac{270 (4675668676672)}{33252567300796594218750}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $270$ out of $33252567300796594218750$ .

$\frac{270 \cdot 4675668676672}{270 \cdot 123157656669617015625}$

Step 8.2.2

Cancel the common factor.

$\frac{270 \cdot 4675668676672}{270 \cdot 123157656669617015625}$

Step 8.2.3

Rewrite the expression.

$\frac{4675668676672}{123157656669617015625}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{4675668676672}{123157656669617015625}$

Decimal Form:

$3.79649045 \cdot 10^{- 8}$