Question

What is `a^(1/2)b^(4/3)c^(3/4)` in radical form?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`a^(1/2)b^(4 xx 1/3)c^(3 xx 1/4)`

We can then 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)`

`a^(1/2)b^(color(red)(4) xx color(blue)(1/3))c^(color(red)(3) xx color(blue)(1/4)) => a^(1/2)(b^color(red)(4))^color(blue)(1/3)(c^color(red)(3))^color(blue)(1/4)`

We can now use rule to write this in radical form:

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

`root(2)(a)root(3)(b^4)root(4)(c^3)`

Or

`sqrt(a)root(3)(b^4)root(4)(c^3)`