What is [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2} ?

The solution to [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2} is 2^{5/6}

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simplify [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2}

simplify

[(2^{2})^{\frac{1}{2}}]^{\frac{1}{3}} \cdot [(2^{3})^{\frac{1}{3}}]^{\frac{1}{2}}

2^{\frac{5}{6}}

Decimal Notation

1.78179 \dots

Solution steps

[(2^{2})^{\frac{1}{2}}]^{\frac{1}{3}} [(2^{3})^{\frac{1}{3}}]^{\frac{1}{2}}

(2^{2})^{\frac{1}{2}} : 2

= [2]^{\frac{1}{3}} ((2^{3})^{\frac{1}{3}})^{\frac{1}{2}}

(2^{3})^{\frac{1}{3}} : 2

= [2]^{\frac{1}{3}} \cdot 2^{\frac{1}{2}}

Apply exponent rule:

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

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

= 2^{\frac{1}{3} + \frac{1}{2}}

Join

\frac{1}{3} + \frac{1}{2} : \frac{5}{6}

= 2^{\frac{5}{6}}

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

(0.1 x y) \cdot (100 x y^{2}) \cdot (0.01 x^{3})

e^{e^{t}} \cdot e^{t}

What is [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2} ?
The solution to [(2^2)^{1/2}]^{1/3}*[(2^3)^{1/3}]^{1/2} is 2^{5/6}