What is e^{1/2-sqrt(6)x}*sqrt(6)e^{1/2+sqrt(6)x} ?

The solution to e^{1/2-sqrt(6)x}*sqrt(6)e^{1/2+sqrt(6)x} is sqrt(6)e

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simplify e^{1/2-sqrt(6)x}*sqrt(6)e^{1/2+sqrt(6)x}

simplify

e^{\frac{1}{2} - 6 x} \cdot 6 e^{\frac{1}{2} + 6 x}

6 e

Decimal Notation

6.65840 \dots

Solution steps

e^{\frac{1}{2} - 6 x} 6 e^{\frac{1}{2} + 6 x}

Apply exponent rule:

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

e^{\frac{1}{2} - 6 x} e^{\frac{1}{2} + 6 x} = e^{\frac{1}{2} - 6 x + \frac{1}{2} + 6 x}

= 6 e^{\frac{1}{2} - 6 x + \frac{1}{2} + 6 x}

Combine the fractions

\frac{1}{2} + \frac{1}{2} : 1

= 6 e^{6 x - 6 x + 1}

e^{1 - 6 x + 6 x} = e

= 6 e

- e^{- x} \cdot 9 e^{3 x}

e^{- \frac{26}{450}}

7.5 \cdot 1 0^{- 1}

1500 \cdot e^{- 2000 \cdot (\frac{1}{513.15} - \frac{1}{289})}

2.97 x 1 0^{- 2}

What is e^{1/2-sqrt(6)x}*sqrt(6)e^{1/2+sqrt(6)x} ?
The solution to e^{1/2-sqrt(6)x}*sqrt(6)e^{1/2+sqrt(6)x} is sqrt(6)e