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Popular >

simplify e^{-x}*(e^{-x})/2

Solution

simplify

e^{- x} \cdot \frac{e ^{- x}}{2}

Solution

\frac{1}{2 e ^{2 x}}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{x}} \cdot \frac{e ^{- x}}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot e ^{- x}}{e ^{x} \cdot 2}

Multiply:

1 \cdot e^{- x} = e^{- x}

= \frac{e ^{- x}}{2 e ^{x}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{- x}}{e ^{x}} = e^{- x - x} = e^{- 2 x}

= \frac{1}{2 e ^{2 x}}

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Frequently Asked Questions (FAQ)

What is e^{-x}*(e^{-x})/2 ?
The solution to e^{-x}*(e^{-x})/2 is 1/(2e^{2x)}