Evaluate 80e^(-0.4(1))+20

$80 e^{- 0.4 (1)} + 20$

Step 1

Simplify each term.

Multiply $- 0.4$ by $1$ .

$80 e^{- 0.4} + 20$

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

$80 \frac{1}{e^{0.4}} + 20$

Combine $80$ and $\frac{1}{e^{0.4}}$ .

$\frac{80}{e^{0.4}} + 20$

Step 2

To write $20$ as a fraction with a common denominator, multiply by $\frac{e^{0.4}}{e^{0.4}}$ .

$\frac{80}{e^{0.4}} + \frac{20 e^{0.4}}{e^{0.4}}$

Step 3

Combine the numerators over the common denominator.

$\frac{80 + 20 e^{0.4}}{e^{0.4}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{80 + 20 e^{0.4}}{e^{0.4}}$

Decimal Form:

$73.62560368 \dots$