What is simplify-ae^{-2x}*ae^{(-x)/2} ?

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

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simplify-ae^{-2x}*ae^{(-x)/2}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

aa = a^{1 + 1}

= - e^{- 2 x} a^{1 + 1} e^{\frac{- x}{2}}

Add the numbers:

1 + 1 = 2

= - e^{- 2 x} a^{2} e^{\frac{- x}{2}}

Apply exponent rule:

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

e^{- 2 x} e^{\frac{- x}{2}} = e^{- 2 x + \frac{- x}{2}}

= - a^{2} e^{- 2 x + \frac{- x}{2}}

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

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

n^{- e}

4.03 \cdot 1 0^{- 3} \cdot 26.79

\frac{2.5678}{0.131}

e^{(- 0.4 \cdot 11)}

What is simplify-ae^{-2x}*ae^{(-x)/2} ?
The solution to simplify-ae^{-2x}*ae^{(-x)/2} is -a^2e^{-(5x)/2}