Precalculus Examples

$\frac{e^{3 x} \cdot e^{- 5}}{e^{2 x}}$

Step 1

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

$\frac{e^{3 x - 5}}{e^{2 x}}$

Step 2

Cancel the common factor of $e^{3 x - 5}$ and $e^{2 x}$ .

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Step 2.1

Factor $e^{2 x}$ out of $e^{3 x - 5}$ .

$\frac{e^{2 x} e^{x - 5}}{e^{2 x}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{e^{2 x} e^{x - 5}}{e^{2 x} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{e^{2 x} e^{x - 5}}{e^{2 x} \cdot 1}$

Step 2.2.3

Rewrite the expression.

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

Step 2.2.4

Divide $e^{x - 5}$ by $1$ .

$e^{x - 5}$