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

The solution to (+3e^3)e^{-5} is 3/(e^2)

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

simplify

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

\frac{3}{e ^{2}}

Solution steps

(3 e^{3}) e^{- 5}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{3} e^{- 5} = e^{3 - 5}

= 3 e^{3 - 5}

Subtract the numbers:

3 - 5 = - 2

= 3 e^{- 2}

Apply exponent rule:

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

e^{- 2} = \frac{1}{e ^{2}}

= 3 \cdot \frac{1}{e ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 3}{e ^{2}}

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{e ^{2}}

y^{- \frac{1}{3} = 4}

1.1 \cdot 10000 \cdot 0.1 \cdot 1 0^{- 6}

\frac{e ^{- k t}}{e ^{- k (t + \frac{t ^{1}}{2})}}

(a x - b y)^{2} (a x + b y)^{2}