Finite Math Examples

$6 {(\frac{4}{5})}^{4} {(\frac{1}{5})}^{0}$

Step 1

Apply the product rule to $\frac{4}{5}$ .

$6 \frac{4^{4}}{5^{4}} {(\frac{1}{5})}^{0}$

Step 2

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

$6 \frac{256}{5^{4}} {(\frac{1}{5})}^{0}$

Step 3

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

$6 (\frac{256}{625}) {(\frac{1}{5})}^{0}$

Step 4

Multiply $6 (\frac{256}{625})$ .

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Step 4.1

Combine $6$ and $\frac{256}{625}$ .

$\frac{6 \cdot 256}{625} {(\frac{1}{5})}^{0}$

Step 4.2

Multiply $6$ by $256$ .

$\frac{1536}{625} {(\frac{1}{5})}^{0}$

$\frac{1536}{625} {(\frac{1}{5})}^{0}$

Step 5

Combine fractions.

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Step 5.1

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

$\frac{1536}{625} \cdot \frac{1^{0}}{5^{0}}$

Step 5.2

Combine.

$\frac{1536 \cdot 1^{0}}{625 \cdot 5^{0}}$

Step 5.3

Anything raised to $0$ is $1$ .

$\frac{1536 \cdot 1}{625 \cdot 5^{0}}$

$\frac{1536 \cdot 1}{625 \cdot 5^{0}}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite $625$ as $5^{4}$ .

$\frac{1536 \cdot 1}{5^{4} \cdot 5^{0}}$

Step 6.2

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

$\frac{1536 \cdot 1}{5^{4 + 0}}$

Step 6.3

Add $4$ and $0$ .

$\frac{1536 \cdot 1}{5^{4}}$

$\frac{1536 \cdot 1}{5^{4}}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $1536$ by $1$ .

$\frac{1536}{5^{4}}$

Step 7.2

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

$\frac{1536}{625}$

$\frac{1536}{625}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1536}{625}$

Decimal Form:

$2.4576$

Mixed Number Form:

$2 \frac{286}{625}$

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