How do you write $4^(2/3) * a^(1/3)$ in radical form?

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Answer 1 · 2017-07-21T03:52:43

See a solution process below:

First, rewrite the $4$ term as:

$4^(2 xx 1/3) * a^(1/3)$

Next, use this rule of exponents to rewrite the $4$ term again:

$x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)$

$(4^2)^(1/3) * a^(1/3) => 16^(1/3) * a^(1/3) => (16a)^(1/3)$

Next, use this rule to put the expression into radical form:

$x^(1/color(red)(n)) = root(color(red)(n))(x)$

$(16a)^(1/color(red)(3)) => root(color(red)(3))(16a)$

If necessary we can rewrite this as:

$root(3)(16a) => root(3)(8 * 2a) => root(3)(8)root(3)(2a) => 2root(3)(2a)$

How do you write 4^(2/3) * a^(1/3) 4^(2/3) * a^(1/3) in radical form?