What is sqrt(e^{-6x)}\times (e^x)^3 ?

The solution to sqrt(e^{-6x)}\times (e^x)^3 is 1

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simplify sqrt(e^{-6x)}\times (e^x)^3

simplify

e^{- 6 x} \cdot (e^{x})^{3}

1

Solution steps

e^{- 6 x} (e^{x})^{3}

e^{- 6 x} : e^{- 3 x}

= e^{- 3 x} (e^{x})^{3}

(e^{x})^{3} : e^{x \cdot 3}

= e^{- 3 x} e^{x \cdot 3}

Apply exponent rule:

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

e^{- 3 x} e^{x \cdot 3} = e^{- 3 x + 3 x}

= e^{- 3 x + x \cdot 3}

Add similar elements:

- 3 x + 3 x = 0

= e^{0}

Apply rule

a^{0} = 1, a \neq = 0

= 1

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What is sqrt(e^{-6x)}\times (e^x)^3 ?
The solution to sqrt(e^{-6x)}\times (e^x)^3 is 1