Calculus Examples

$4 e^{2} + 4 e^{- 2}$

Step 1

Simplify each term.

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Step 1.1

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

$4 e^{2} + 4 \frac{1}{e^{2}}$

Step 1.2

Combine $4$ and $\frac{1}{e^{2}}$ .

$4 e^{2} + \frac{4}{e^{2}}$

Step 2

To write $4 e^{2}$ as a fraction with a common denominator, multiply by $\frac{e^{2}}{e^{2}}$ .

$\frac{4 e^{2} e^{2}}{e^{2}} + \frac{4}{e^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{4 e^{2} e^{2} + 4}{e^{2}}$

Step 4

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

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Step 4.1

Move $e^{2}$ .

$\frac{4 (e^{2} e^{2}) + 4}{e^{2}}$

Step 4.2

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

$\frac{4 e^{2 + 2} + 4}{e^{2}}$

Step 4.3

Add $2$ and $2$ .

$\frac{4 e^{4} + 4}{e^{2}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 e^{4} + 4}{e^{2}}$

Decimal Form:

$30.09756552 \dots$