Finite Math Examples

$e^{- 0.7} - e^{- 1.4}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{e^{0.7}} - e^{- 1.4}$

Step 1.2

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

$\frac{1}{e^{0.7}} - \frac{1}{e^{1.4}}$

Step 2

To write $\frac{1}{e^{0.7}}$ as a fraction with a common denominator, multiply by $\frac{e^{0.7}}{e^{0.7}}$ .

$\frac{1}{e^{0.7}} \cdot \frac{e^{0.7}}{e^{0.7}} - \frac{1}{e^{1.4}}$

Step 3

Write each expression with a common denominator of $e^{1.4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{e^{0.7}}$ by $\frac{e^{0.7}}{e^{0.7}}$ .

$\frac{e^{0.7}}{e^{0.7} e^{0.7}} - \frac{1}{e^{1.4}}$

Step 3.2

Multiply $e^{0.7}$ by $e^{0.7}$ by adding the exponents.

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Step 3.2.1

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

$\frac{e^{0.7}}{e^{0.7 + 0.7}} - \frac{1}{e^{1.4}}$

Step 3.2.2

Add $0.7$ and $0.7$ .

$\frac{e^{0.7}}{e^{1.4}} - \frac{1}{e^{1.4}}$

Step 4

Combine the numerators over the common denominator.

$\frac{e^{0.7} - 1}{e^{1.4}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{0.7} - 1}{e^{1.4}}$

Decimal Form:

$0.24998833 \dots$