What is 10e^{-x}(-e^4x) ?

The solution to 10e^{-x}(-e^4x) is -10e^{-x+4}x

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simplify 10e^{-x}(-e^4x)

simplify

10 e^{- x} (- e^{4} x)

- 10 e^{- x + 4} x

Solution steps

10 e^{- x} (- e^{4} x)

Apply exponent rule:

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

= 10 \cdot \frac{1}{e ^{x}} (- e^{4} x)

Remove parentheses:

(- a) = - a

= - 10 \cdot \frac{1}{e ^{x}} e^{4} x

Multiply fractions:

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

= - \frac{1 \cdot 10 e ^{4} x}{e ^{x}}

Multiply the numbers:

1 \cdot 10 = 10

= - \frac{10 e ^{4} x}{e ^{x}}

Apply exponent rule:

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

\frac{e ^{4}}{e ^{x}} = e^{4 - x}

= - 10 e^{- x + 4} x

1.2 \cdot (18023.6 + 17438.6) \cdot (0.794 \cdot 1 0^{- 3}) \cdot 13

(4 π \cdot 1 0^{- 7} \cdot 2500) \cdot (1.8 \cdot 1 0^{- 3})

1.06 \cdot 1 0^{- 10}

10 π 1 0^{9} 2.81 \cdot 1 0^{- 17} (1) - 1

e^{- 500000}