Finite Math Examples

${1.008}^{n} (\frac{1 - {1.008}^{n}}{1 - 1.008})$

Step 1

Simplify terms.

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Step 1.1

Subtract $1.008$ from $1$ .

${1.008}^{n} \frac{1 - {1.008}^{n}}{- 0.008}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Move the negative in front of the fraction.

${1.008}^{n} (- \frac{1 - {1.008}^{n}}{0.008})$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- {1.008}^{n} \frac{1 - {1.008}^{n}}{0.008}$

Step 1.3

Cancel the common factor of $0.008$ .

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Step 1.3.1

Factor $0.008$ out of $- {1.008}^{n}$ .

$0.008 (- 125 \cdot {1.008}^{n}) \frac{1 - {1.008}^{n}}{0.008}$

Step 1.3.2

Cancel the common factor.

$0.008 (- 125 \cdot {1.008}^{n}) \frac{1 - {1.008}^{n}}{0.008}$

Step 1.3.3

Rewrite the expression.

$- 125 \cdot {1.008}^{n} (1 - {1.008}^{n})$

Step 1.4

Apply the distributive property.

$- 125 \cdot {1.008}^{n} \cdot 1 - 125 \cdot {1.008}^{n} (- {1.008}^{n})$

Step 1.5

Simplify the expression.

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Step 1.5.1

Multiply $- 125$ by $1$ .

$- 125 \cdot {1.008}^{n} - 125 \cdot {1.008}^{n} (- {1.008}^{n})$

Step 1.5.2

Rewrite using the commutative property of multiplication.

$- 125 \cdot {1.008}^{n} - 125 \cdot - 1 \cdot {1.008}^{n} \cdot {1.008}^{n}$

Step 2

Simplify each term.

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Step 2.1

Multiply ${1.008}^{n}$ by ${1.008}^{n}$ by adding the exponents.

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Step 2.1.1

Move ${1.008}^{n}$ .

$- 125 \cdot {1.008}^{n} - 125 \cdot - 1 \cdot ({1.008}^{n} \cdot {1.008}^{n})$

Step 2.1.2

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

$- 125 \cdot {1.008}^{n} - 125 \cdot - 1 \cdot {1.008}^{n + n}$

Step 2.1.3

Add $n$ and $n$ .

$- 125 \cdot {1.008}^{n} - 125 \cdot - 1 \cdot {1.008}^{2 n}$

Step 2.2

Multiply $- 125$ by $- 1$ .

$- 125 \cdot {1.008}^{n} + 125 \cdot {1.008}^{2 n}$