What is ((-e^{-3x^2}+c*2)/(2e^{-3x^2)})^{-1/3} ?

The solution to ((-e^{-3x^2}+c*2)/(2e^{-3x^2)})^{-1/3} is (2^{1/3}e^{-x^2})/((2c-e^{-3x^2))^{1/3}}

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simplify ((-e^{-3x^2}+c*2)/(2e^{-3x^2)})^{-1/3}

simplify

(\frac{- e ^{- 3 x^{2}} + c \cdot 2}{2 e ^{- 3 x^{2}}})^{- \frac{1}{3}}

\frac{2 ^{\frac{1}{3}} e ^{- x^{2}}}{( 2 c - e ^{- 3 x^{2}} ) ^{\frac{1}{3}}}

Solution steps

(\frac{- e ^{- 3 x^{2}} + c \cdot 2}{2 e ^{- 3 x^{2}}})^{- \frac{1}{3}}

Apply exponent rule:

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

= \frac{1}{( \frac{- e ^{- 3 x^{2}} + c \cdot 2}{2 e ^{- 3 x^{2}}} ) ^{\frac{1}{3}}}

(\frac{- e ^{- 3 x^{2}} + c \cdot 2}{2 e ^{- 3 x^{2}}})^{\frac{1}{3}} = \frac{( - e ^{- 3 x^{2}} + 2 c ) ^{\frac{1}{3}}}{2 ^{\frac{1}{3}} e ^{- x^{2}}}

= \frac{1}{\frac{( - e ^{- 3 x^{2}} + 2 c ) ^{\frac{1}{3}}}{2 ^{\frac{1}{3}} e ^{- x^{2}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2 ^{\frac{1}{3}} e ^{- x^{2}}}{( - e ^{- 3 x^{2}} + c \cdot 2 ) ^{\frac{1}{3}}}

1.6 \cdot 1 0^{- 8} \cdot \frac{x}{1.6775 \cdot 1 0 ^{- 5}}

e^{- 5 t} H (- t - 1)

15 e^{- 0.15 (4.62)}

0.1 \cdot e^{- 0.1}

What is ((-e^{-3x^2}+c*2)/(2e^{-3x^2)})^{-1/3} ?
The solution to ((-e^{-3x^2}+c*2)/(2e^{-3x^2)})^{-1/3} is (2^{1/3}e^{-x^2})/((2c-e^{-3x^2))^{1/3}}