What is 4x^3*1/9 e^{-3x} ?

The solution to 4x^3*1/9 e^{-3x} is (4x^3)/(9e^{3x)}

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simplify 4x^3*1/9 e^{-3x}

simplify

4 x^{3} \cdot \frac{1}{9} e^{- 3 x}

\frac{4 x ^{3}}{9 e ^{3 x}}

Solution steps

4 x^{3} \frac{1}{9} e^{- 3 x}

Apply exponent rule:

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

= 4 \cdot \frac{1}{9} \cdot \frac{1}{e ^{3 x}} x^{3}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot 4 x ^{3}}{9 e ^{3 x}}

Multiply the numbers:

1 \cdot 1 \cdot 4 = 4

= \frac{4 x ^{3}}{9 e ^{3 x}}

(4 \cdot 1 0^{3}) (1.6 \cdot 1 0^{- 19})

e^{- 100} \cdot 10 0^{95}

(1.2 \cdot 1 0^{- 5}) (1.2 \cdot 1 0^{- 3})

e^{4} (e^{3})

2 (2 \cdot (- 1)^{k})