Calculus Examples

$e^{2} - e^{- 3}$

Step 1

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

$e^{2} - \frac{1}{e^{3}}$

Step 2

To write $e^{2}$ as a fraction with a common denominator, multiply by $\frac{e^{3}}{e^{3}}$ .

$\frac{e^{2} e^{3}}{e^{3}} - \frac{1}{e^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{e^{2} e^{3} - 1}{e^{3}}$

Step 4

Multiply $e^{2}$ by $e^{3}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

$\frac{e^{2 + 3} - 1}{e^{3}}$

Step 4.2

Add $2$ and $3$ .

$\frac{e^{5} - 1}{e^{3}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{e^{5} - 1}{e^{3}}$

Decimal Form:

$7.33926903 \dots$