Algebra Examples

$- 9^{- 2} + 3^{- 3} + {(- 7)}^{0}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{1}{9^{2}} + 3^{- 3} + {(- 7)}^{0}$

Step 1.2

Raise $9$ to the power of $2$ .

$- \frac{1}{81} + 3^{- 3} + {(- 7)}^{0}$

Step 1.3

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

$- \frac{1}{81} + \frac{1}{3^{3}} + {(- 7)}^{0}$

Step 1.4

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

$- \frac{1}{81} + \frac{1}{27} + {(- 7)}^{0}$

Step 1.5

Anything raised to $0$ is $1$ .

$- \frac{1}{81} + \frac{1}{27} + 1$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{27}$ by $\frac{3}{3}$ .

$- \frac{1}{81} + \frac{1}{27} \cdot \frac{3}{3} + 1$

Step 2.2

Multiply $\frac{1}{27}$ by $\frac{3}{3}$ .

$- \frac{1}{81} + \frac{3}{27 \cdot 3} + 1$

Step 2.3

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

$- \frac{1}{81} + \frac{3}{27 \cdot 3} + \frac{1}{1}$

Step 2.4

Multiply $\frac{1}{1}$ by $\frac{81}{81}$ .

$- \frac{1}{81} + \frac{3}{27 \cdot 3} + \frac{1}{1} \cdot \frac{81}{81}$

Step 2.5

Multiply $\frac{1}{1}$ by $\frac{81}{81}$ .

$- \frac{1}{81} + \frac{3}{27 \cdot 3} + \frac{81}{81}$

Step 2.6

Reorder the factors of $27 \cdot 3$ .

$- \frac{1}{81} + \frac{3}{3 \cdot 27} + \frac{81}{81}$

Step 2.7

Multiply $3$ by $27$ .

$- \frac{1}{81} + \frac{3}{81} + \frac{81}{81}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 1 + 3 + 81}{81}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $- 1$ and $3$ .

$\frac{2 + 81}{81}$

Step 4.2

Add $2$ and $81$ .

$\frac{83}{81}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{81}$

Decimal Form:

$1.02469135 \dots$

Mixed Number Form:

$1 \frac{2}{81}$