Calculus Examples

$e - e^{- 4}$

Step 1

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

$e - \frac{1}{e^{4}}$

Step 2

To write $e$ as a fraction with a common denominator, multiply by $\frac{e^{4}}{e^{4}}$ .

$\frac{e e^{4}}{e^{4}} - \frac{1}{e^{4}}$

Step 3

Combine the numerators over the common denominator.

$\frac{e e^{4} - 1}{e^{4}}$

Step 4

Multiply $e$ by $e^{4}$ by adding the exponents.

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Step 4.1

Multiply $e$ by $e^{4}$ .

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Step 4.1.1

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

$\frac{e^{1} e^{4} - 1}{e^{4}}$

Step 4.1.2

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

$\frac{e^{1 + 4} - 1}{e^{4}}$

Step 4.2

Add $1$ and $4$ .

$\frac{e^{5} - 1}{e^{4}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{5} - 1}{e^{4}}$

Decimal Form:

$2.69996618 \dots$