Algebra Examples

$18 \cdot {(\frac{1}{9})}^{2} - 11 \cdot \frac{1}{9}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{9}$ .

$18 \cdot \frac{1^{2}}{9^{2}} - 11 \cdot \frac{1}{9}$

Step 1.2

One to any power is one.

$18 \cdot \frac{1}{9^{2}} - 11 \cdot \frac{1}{9}$

Step 1.3

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

$18 \cdot \frac{1}{81} - 11 \cdot \frac{1}{9}$

Step 1.4

Cancel the common factor of $9$ .

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Step 1.4.1

Factor $9$ out of $18$ .

$9 (2) \cdot \frac{1}{81} - 11 \cdot \frac{1}{9}$

Step 1.4.2

Factor $9$ out of $81$ .

$9 \cdot 2 \cdot \frac{1}{9 \cdot 9} - 11 \cdot \frac{1}{9}$

Step 1.4.3

Cancel the common factor.

$9 \cdot 2 \cdot \frac{1}{9 \cdot 9} - 11 \cdot \frac{1}{9}$

Step 1.4.4

Rewrite the expression.

$2 \cdot \frac{1}{9} - 11 \cdot \frac{1}{9}$

Step 1.5

Combine $2$ and $\frac{1}{9}$ .

$\frac{2}{9} - 11 \cdot \frac{1}{9}$

Step 1.6

Combine $- 11$ and $\frac{1}{9}$ .

$\frac{2}{9} + \frac{- 11}{9}$

Step 1.7

Move the negative in front of the fraction.

$\frac{2}{9} - \frac{11}{9}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 - 11}{9}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $11$ from $2$ .

$\frac{- 9}{9}$

Step 2.2.2

Divide $- 9$ by $9$ .

$- 1$