Finite Math Examples

$6 - 5 - 3^{2 - 3}$

Step 1

Simplify each term.

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Step 1.1

Subtract $3$ from $2$ .

$6 - 5 - 3^{- 1}$

Step 1.2

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

$6 - 5 - \frac{1}{3}$

Step 2

Find the common denominator.

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Step 2.1

Write $6$ as a fraction with denominator $1$ .

$\frac{6}{1} - 5 - \frac{1}{3}$

Step 2.2

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{6}{1} \cdot \frac{3}{3} - 5 - \frac{1}{3}$

Step 2.3

Multiply $\frac{6}{1}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} - 5 - \frac{1}{3}$

Step 2.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{6 \cdot 3}{3} + \frac{- 5}{1} - \frac{1}{3}$

Step 2.5

Multiply $\frac{- 5}{1}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{- 5}{1} \cdot \frac{3}{3} - \frac{1}{3}$

Step 2.6

Multiply $\frac{- 5}{1}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 3}{3} + \frac{- 5 \cdot 3}{3} - \frac{1}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 - 5 \cdot 3 - 1}{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $6$ by $3$ .

$\frac{18 - 5 \cdot 3 - 1}{3}$

Step 4.2

Multiply $- 5$ by $3$ .

$\frac{18 - 15 - 1}{3}$

Step 5

Simplify by subtracting numbers.

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Step 5.1

Subtract $15$ from $18$ .

$\frac{3 - 1}{3}$

Step 5.2

Subtract $1$ from $3$ .

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$