What is (\sqrt[(3)]{2^{3x-1}})^{1/(x-3)} ?

The solution to (\sqrt[(3)]{2^{3x-1}})^{1/(x-3)} is 2^{(3x-1)/(3(x-3))}

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simplify (\sqrt[(3)]{2^{3x-1}})^{1/(x-3)}

simplify

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

Solution steps

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{3 x - 1}{3} \cdot \frac{1}{x - 3}}

Simplify

\frac{3 x - 1}{3} \cdot \frac{1}{x - 3} : \frac{3 x - 1}{3 ( x - 3 )}

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

e^{- \frac{17}{3}} \cdot (- 24)

- 1

6.282 \cdot 1 0^{- 5}

(2.192 \cdot 1 0^{- 7}) x^{5}

(32.1 \cdot 1 0^{3}) e^{- 2 \cdot (2.78 \cdot 1 0^{- 7}) \cdot 600}

What is (\sqrt[(3)]{2^{3x-1}})^{1/(x-3)} ?
The solution to (\sqrt[(3)]{2^{3x-1}})^{1/(x-3)} is 2^{(3x-1)/(3(x-3))}