Finite Math Examples

$\frac{49}{5} \cdot {(\frac{5}{7})}^{5}$

Step 1

Apply the product rule to $\frac{5}{7}$ .

$\frac{49}{5} \cdot \frac{5^{5}}{7^{5}}$

Step 2

Combine.

$\frac{49 \cdot 5^{5}}{5 \cdot 7^{5}}$

Step 3

Cancel the common factor of $5^{5}$ and $5$ .

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Step 3.1

Factor $5$ out of $49 \cdot 5^{5}$ .

$\frac{5 (49 \cdot 5^{4})}{5 \cdot 7^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $5 \cdot 7^{5}$ .

$\frac{5 (49 \cdot 5^{4})}{5 (7^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (49 \cdot 5^{4})}{5 \cdot 7^{5}}$

Step 3.2.3

Rewrite the expression.

$\frac{49 \cdot 5^{4}}{7^{5}}$

$\frac{49 \cdot 5^{4}}{7^{5}}$

$\frac{49 \cdot 5^{4}}{7^{5}}$

Step 4

Simplify the expression.

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Step 4.1

Raise $5$ to the power of $4$ .

$\frac{49 \cdot 625}{7^{5}}$

Step 4.2

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

$\frac{49 \cdot 625}{16807}$

Step 4.3

Multiply $49$ by $625$ .

$\frac{30625}{16807}$

$\frac{30625}{16807}$

Step 5

Cancel the common factor of $30625$ and $16807$ .

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Step 5.1

Factor $49$ out of $30625$ .

$\frac{49 (625)}{16807}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $49$ out of $16807$ .

$\frac{49 \cdot 625}{49 \cdot 343}$

Step 5.2.2

Cancel the common factor.

$\frac{49 \cdot 625}{49 \cdot 343}$

Step 5.2.3

Rewrite the expression.

$\frac{625}{343}$

$\frac{625}{343}$

$\frac{625}{343}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{625}{343}$

Decimal Form:

$1.82215743 \dots$

Mixed Number Form:

$1 \frac{282}{343}$

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