Evaluate 1-e^-3

$1 - e^{- 3}$

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

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

Simplify the expression.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Rewrite $1$ as $1^{3}$ .

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

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = e$ and $b = 1$ .

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

Simplify.

Multiply $e$ by $1$ .

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

One to any power is one.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.95021293 \dots$

Evaluate 1-e^-3

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