What is sqrt((2-x^{2/3))^3} ?

The solution to sqrt((2-x^{2/3))^3} is (-x^{2/3}+2)^{3/2}

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simplify sqrt((2-x^{2/3))^3}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

assuming

a \geq 0

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

3 \cdot \frac{1}{2} = \frac{3}{2}

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

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

9 e^{- 108}

e^{- \frac{5}{10}}

e^{- (0.2)^{2}}

\frac{5}{2} e^{- \frac{- 3.1606}{2}}

What is sqrt((2-x^{2/3))^3} ?
The solution to sqrt((2-x^{2/3))^3} is (-x^{2/3}+2)^{3/2}