What is \sqrt[6]{(2ab)^2} ?

The solution to \sqrt[6]{(2ab)^2} is cube root of 2}\sqrt[3]{ab

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simplify \sqrt[6]{(2ab)^2}

simplify

6 (2 ab)^{2}

32 3 ab

Solution steps

6 (2 ab)^{2}

Apply radical rule:

n a = a^{\frac{1}{n}}

= ((2 ab)^{2})^{\frac{1}{6}}

Apply exponent rule:

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

assuming

a \geq 0

= (2 ab)^{2 \cdot \frac{1}{6}}

2 \cdot \frac{1}{6} = \frac{1}{3}

= (2 ab)^{\frac{1}{3}}

a^{\frac{1}{n}} = n a

= 3 2 ab

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= 32 3 ab

e^{- \frac{4.5}{6}}

(4 x^{2} y^{2}) (3 x y^{3})

5.46 x^{- 0.278}

2500 \cdot 1.9 6^{2} \cdot 0.5 \cdot 0.5

(7 \cdot 1 0^{5}) (4 \cdot 1 0^{9})

What is \sqrt[6]{(2ab)^2} ?
The solution to \sqrt[6]{(2ab)^2} is cube root of 2}\sqrt[3]{ab