Finite Math Examples

$A (2) = 100 {(3)}^{- 0.5 \cdot 2}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.5$ by $2$ .

$A (2) = 100 \cdot 3^{- 1}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$A (2) = 100 \cdot \frac{1}{3}$

Step 1.3

Combine $100$ and $\frac{1}{3}$ .

$A (2) = \frac{100}{3}$

Step 2

Divide each term in $A (2) = \frac{100}{3}$ by $2$ and simplify.

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Step 2.1

Divide each term in $A (2) = \frac{100}{3}$ by $2$ .

$\frac{A (2)}{2} = \frac{\frac{100}{3}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \cdot 2}{2} = \frac{\frac{100}{3}}{2}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{\frac{100}{3}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$A = \frac{100}{3} \cdot \frac{1}{2}$

Step 2.3.2

Cancel the common factor of $2$ .

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Step 2.3.2.1

Factor $2$ out of $100$ .

$A = \frac{2 (50)}{3} \cdot \frac{1}{2}$

Step 2.3.2.2

Cancel the common factor.

$A = \frac{2 \cdot 50}{3} \cdot \frac{1}{2}$

Step 2.3.2.3

Rewrite the expression.

$A = \frac{50}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$A = \frac{50}{3}$

Decimal Form:

$A = 16.\overline{6}$

Mixed Number Form:

$A = 16 \frac{2}{3}$