Finite Math Examples

$a \cdot 6 = 6250 \cdot {(\frac{1}{5})}^{6 - 1}$

Step 1

Simplify.

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Step 1.1

Subtract $1$ from $6$ .

$a \cdot 6 = 6250 \cdot {(\frac{1}{5})}^{5}$

Step 1.2

Apply the product rule to $\frac{1}{5}$ .

$a \cdot 6 = 6250 \cdot \frac{1^{5}}{5^{5}}$

Step 1.3

One to any power is one.

$a \cdot 6 = 6250 \cdot \frac{1}{5^{5}}$

Step 1.4

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

$a \cdot 6 = 6250 \cdot \frac{1}{3125}$

Step 1.5

Cancel the common factor of $3125$ .

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Step 1.5.1

Factor $3125$ out of $6250$ .

$a \cdot 6 = 3125 (2) \cdot \frac{1}{3125}$

Step 1.5.2

Cancel the common factor.

$a \cdot 6 = 3125 \cdot 2 \cdot \frac{1}{3125}$

Step 1.5.3

Rewrite the expression.

$a \cdot 6 = 2$

$a \cdot 6 = 2$

$a \cdot 6 = 2$

Step 2

Divide each term in $a \cdot 6 = 2$ by $6$ and simplify.

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Step 2.1

Divide each term in $a \cdot 6 = 2$ by $6$ .

$\frac{a \cdot 6}{6} = \frac{2}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a \cdot 6}{6} = \frac{2}{6}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a = \frac{2}{6}$

$a = \frac{2}{6}$

$a = \frac{2}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ and $6$ .

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Step 2.3.1.1

Factor $2$ out of $2$ .

$a = \frac{2 (1)}{6}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $6$ .

$a = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.3.1.2.2

Cancel the common factor.

$a = \frac{2 \cdot 1}{2 \cdot 3}$

Step 2.3.1.2.3

Rewrite the expression.

$a = \frac{1}{3}$

$a = \frac{1}{3}$

$a = \frac{1}{3}$

$a = \frac{1}{3}$

$a = \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{3}$

Decimal Form:

$a = 0.\overline{3}$

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