What is (1/(1+e^x))(e^{-x}) ?

The solution to (1/(1+e^x))(e^{-x}) is 1/(e^x(e^x+1))

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simplify (1/(1+e^x))(e^{-x})

simplify

(\frac{1}{1 + e ^{x}}) (e^{- x})

\frac{1}{e ^{x} ( e ^{x} + 1 )}

Solution steps

(\frac{1}{1 + e ^{x}}) (e^{- x})

Apply exponent rule:

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

= \frac{1}{e ^{x} + 1} \cdot \frac{1}{e ^{x}}

Multiply fractions:

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

= \frac{1 \cdot 1}{( 1 + e ^{x} ) e ^{x}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{e ^{x} ( e ^{x} + 1 )}

\frac{a ^{m}}{b ^{m}}

\frac{( - 99 ) ^{5}}{9 ^{5}}

5 e^{- (2)^{2}}

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