How do you change $a^(1/2)b^(4/3)c^(3/4)$ into radical form?

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Answer 1 · 2017-05-20T20:13:02

See a solution process below:

First, we can use this rule of exponents to put the $a$ term into radical form:

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

$a^(1/color(red)(2))b^(4/3)c^(3/4) => (root(color(red)(2))(a))b^(4/3)c^(3/4) => (sqrt(a))b^(4/3)c^(3/4)$

Next, we can use this rule of exponents to rewrite the $b$ and $c$ terms:

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

$(sqrt(a))b^(4/3)c^(3/4) => (sqrt(a))b^(color(red)(4) xx color(blue0)(1/3))c^(color(red)(3) xx color(blue)(1/4)) => sqrt(a)(b^4)^(1/3)(c^3)^(1/4)$

We can again use this rule of exponents to put the $b$ and $c$ terms in radical form:

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

$sqrt(a)(b^4)^(1/color(red)(3))(c^3)^(1/color(red)(4)) => sqrt(a)root(color(red)(3))(b^4)root(color(red)(4))(c^3)$

How do you change a^(1/2)b^(4/3)c^(3/4)a^(1/2)b^(4/3)c^(3/4) into radical form?