Finite Math Examples

${(\frac{- 2}{5})}^{- 4}$

Step 1

Move the negative in front of the fraction.

${(- \frac{2}{5})}^{- 4}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{5}{2})}^{4}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $- \frac{5}{2}$ .

${(- 1)}^{4} {(\frac{5}{2})}^{4}$

Step 3.2

Apply the product rule to $\frac{5}{2}$ .

${(- 1)}^{4} \frac{5^{4}}{2^{4}}$

Step 4

Raise $- 1$ to the power of $4$ .

$1 \frac{5^{4}}{2^{4}}$

Step 5

Multiply $\frac{5^{4}}{2^{4}}$ by $1$ .

$\frac{5^{4}}{2^{4}}$

Step 6

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

$\frac{625}{2^{4}}$

Step 7

Raise $2$ to the power of $4$ .

$\frac{625}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{625}{16}$

Decimal Form:

$39.0625$

Mixed Number Form:

$39 \frac{1}{16}$