Finite Math Examples

$3^{6} - 3^{- 3}$

Step 1

Simplify each term.

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Step 1.1

Raise $3$ to the power of $6$ .

$729 - 3^{- 3}$

Step 1.2

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

$729 - \frac{1}{3^{3}}$

Step 1.3

Raise $3$ to the power of $3$ .

$729 - \frac{1}{27}$

Step 2

To write $729$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$729 \cdot \frac{27}{27} - \frac{1}{27}$

Step 3

Combine $729$ and $\frac{27}{27}$ .

$\frac{729 \cdot 27}{27} - \frac{1}{27}$

Step 4

Combine the numerators over the common denominator.

$\frac{729 \cdot 27 - 1}{27}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $729$ by $27$ .

$\frac{19683 - 1}{27}$

Step 5.2

Subtract $1$ from $19683$ .

$\frac{19682}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19682}{27}$

Decimal Form:

$728.\overline{962}$

Mixed Number Form:

$728 \frac{26}{27}$