What is e^{-3x}(1+3e^{-x})^5 ?

The solution to e^{-3x}(1+3e^{-x})^5 is ((3e^{-x}+1)^5)/(e^{3x)}

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simplify e^{-3x}(1+3e^{-x})^5

simplify

e^{- 3 x} (1 + 3 e^{- x})^{5}

\frac{( 3 e ^{- x} + 1 ) ^{5}}{e ^{3 x}}

Solution steps

e^{- 3 x} (1 + 3 e^{- x})^{5}

Apply exponent rule:

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

= \frac{1}{e ^{3 x}} (3 e^{- x} + 1)^{5}

Multiply fractions:

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

= \frac{1 \cdot ( 1 + 3 e ^{- x} ) ^{5}}{e ^{3 x}}

Multiply:

1 \cdot (1 + 3 e^{- x})^{5} = (1 + 3 e^{- x})^{5}

= \frac{( 1 + 3 e ^{- x} ) ^{5}}{e ^{3 x}}

2.45 \cdot 1 0^{- 6}

e^{- 2.76}

1.2 \cdot 15 \cdot 1 0^{- 6} \cdot 0.1

\frac{30}{11}

e^{- 2.64}

What is e^{-3x}(1+3e^{-x})^5 ?
The solution to e^{-3x}(1+3e^{-x})^5 is ((3e^{-x}+1)^5)/(e^{3x)}