Pre-Algebra Examples

$\frac{1}{10} \cdot (11^{k} - 1) + 11^{k}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{10} \cdot 11^{k} + \frac{1}{10} \cdot - 1 + 11^{k}$

Step 1.2

Combine $\frac{1}{10}$ and $11^{k}$ .

$\frac{11^{k}}{10} + \frac{1}{10} \cdot - 1 + 11^{k}$

Step 1.3

Combine $\frac{1}{10}$ and $- 1$ .

$\frac{11^{k}}{10} + \frac{- 1}{10} + 11^{k}$

Step 1.4

Move the negative in front of the fraction.

$\frac{11^{k}}{10} - \frac{1}{10} + 11^{k}$

Step 2

To write $11^{k}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{11^{k}}{10} + 11^{k} \cdot \frac{10}{10} - \frac{1}{10}$

Step 3

Combine $11^{k}$ and $\frac{10}{10}$ .

$\frac{11^{k}}{10} + \frac{11^{k} \cdot 10}{10} - \frac{1}{10}$

Step 4

Combine the numerators over the common denominator.

$\frac{11^{k} + 11^{k} \cdot 10}{10} - \frac{1}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{11^{k} + 11^{k} \cdot 10 - 1}{10}$

Step 6

Move $10$ to the left of $11^{k}$ .

$\frac{11^{k} + 10 \cdot 11^{k} - 1}{10}$

Step 7

Add $11^{k}$ and $10 \cdot 11^{k}$ .

$\frac{11 \cdot 11^{k} - 1}{10}$

Step 8

Multiply $11$ by $11^{k}$ .

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Step 8.1

Raise $11$ to the power of $1$ .

$\frac{11^{1} \cdot 11^{k} - 1}{10}$

Step 8.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{11^{1 + k} - 1}{10}$