How do you simplify ${(4^{\frac{1}{3}})}^{\frac{3}{2}}$ $(4^(1/3))^(3/2)$ ?

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How do you simplify ${(4^{\frac{1}{3}})}^{\frac{3}{2}}$ $(4^(1/3))^(3/2)$ ?

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Answer 1 · 2017-02-01T12:36:19

$= \pm 2$ $=+-2$

Explanation:

${(4^{\frac{1}{3}})}^{\frac{3}{2}}$ $(4^(1/3))^(3/2)$

$= 4^{\frac{1}{3} \times \frac{3}{2}}$ $=4^(1/3 times3/2)$

$= 4^{\frac{1}{2}}$ $=4^(1/2)$

$= \sqrt{4}$ $=sqrt4$

$= \pm 2$ $=+-2$

Answer 2 · 2017-02-01T12:36:24

See the entire simplification process below:

Explanation:

First, use this rule for exponents to start the simplification process:

${(x^{a})}^{b} = x^{a \times b}$ $(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

${(4^{\frac{1}{3}})}^{\frac{3}{2}} = 4^{\frac{1}{3} \times \frac{3}{2}} = 4^{\frac{3}{6}} = 4^{\frac{1}{2}} = 2$ $(4^color(red)(1/3))^color(blue)(3/2) = 4^(color(red)(1/3) xx color(blue)(3/2)) = 4^(3/6) = 4^(1/2) = 2$

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How do you simplify ${(4^{\frac{1}{3}})}^{\frac{3}{2}}$ $(4^(1/3))^(3/2)$ ?

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