What is 5x^{5/2}*e^{-x} ?

The solution to 5x^{5/2}*e^{-x} is (5x^{5/2})/(e^x)

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simplify 5x^{5/2}*e^{-x}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

= 5 \cdot \frac{1}{e ^{x}} x^{\frac{5}{2}}

Multiply fractions:

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

= \frac{1 \cdot 5 x ^{\frac{5}{2}}}{e ^{x}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5 x ^{\frac{5}{2}}}{e ^{x}}

5.817731355 x 1 0^{- 3}

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3^{8 \circ} 3