Finite Math Examples

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

Step 1

Move ${(5 a^{- 2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply $a^{2}$ by $a^{- 2}$ by adding the exponents.

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Step 2.1.1

Move $a^{- 2}$ .

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

Step 2.1.2

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

$\frac{1}{5 a^{- 2 + 2} \cdot 5}$

Step 2.1.3

Add $- 2$ and $2$ .

$\frac{1}{5 a^{0} \cdot 5}$

Step 2.2

Simplify $5 a^{0} \cdot 5$ .

$\frac{1}{5 \cdot 5}$

Step 3

Multiply $5$ by $5$ .

$\frac{1}{25}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$