What is (e^{5x})^2(-5e^{-5t}) ?

The solution to (e^{5x})^2(-5e^{-5t}) is -5e^{10x-5t}

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simplify (e^{5x})^2(-5e^{-5t})

simplify

(e^{5 x})^{2} (- 5 e^{- 5 t})

- 5 e^{10 x - 5 t}

Solution steps

(e^{5 x})^{2} (- 5 e^{- 5 t})

(e^{5 x})^{2} : e^{10 x}

= e^{10 x} (- 5 e^{- 5 t})

Remove parentheses:

(- a) = - a

= - e^{10 x} \cdot 5 e^{- 5 t}

Apply exponent rule:

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

e^{10 x} e^{- 5 t} = e^{10 x - 5 t}

= - 5 e^{10 x - 5 t}

4.33 \cdot 1 0^{- 22}

5 e^{- 0.00025 (4000)} (600)

18.05 \cdot 3.6 \cdot 1 0^{- 6}

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

What is (e^{5x})^2(-5e^{-5t}) ?
The solution to (e^{5x})^2(-5e^{-5t}) is -5e^{10x-5t}