What is (\sqrt[4]{2a^3b^2})^2 ?

The solution to (\sqrt[4]{2a^3b^2})^2 is sqrt(2)absqrt(a)

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simplify (\sqrt[4]{2a^3b^2})^2

simplify

2 ab a

Solution steps

Apply radical rule:

= ((2 a^{3} b^{2})^{\frac{1}{4}})^{2}

Apply exponent rule:

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

= (2 a^{3} b^{2})^{\frac{1}{4} \cdot 2}

\frac{1}{4} \cdot 2 = \frac{1}{2}

= (2 a^{3} b^{2})^{\frac{1}{2}}

a^{\frac{1}{2}} = a

= 2 a^{3} b^{2}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 2 a^{3} b^{2}

Apply exponent rule:

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

= 2 a^{2} a^{1} b^{2}

Apply radical rule:

a \cdot b = a b

= 2 a^{2} a^{1} b^{2}

Apply radical rule:

assuming

a \geq 0

a^{2} = a

= 2 a a^{1} b^{2}

Apply radical rule:

assuming

a \geq 0

b^{2} = b

= 2 ab a^{1}

Apply rule

a^{1} = a

a^{1} = a

= 2 ab a

- e^{- 2 x}

(m + 2)^{3} (m - 2)^{3}

y^{2} x^{2}

What is (\sqrt[4]{2a^3b^2})^2 ?
The solution to (\sqrt[4]{2a^3b^2})^2 is sqrt(2)absqrt(a)