Question

How do you write the exponential expression `3x^(3/8)` in radical form?

Answer 1

See the entire solution process below:

Explanation:

First we can use this rule of exponents to rewrite this expression:

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

`3x^(3/8) = 3x^(color(red)(3) xx color(blue)(1/8)) = 3(x^color(red)(3))^color(blue)(1/8)`

Now, we can use this rule of radicals and exponents to write this expression in radical form:

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

`3(x^3)^(1/color(red)(8)) = 3root(color(red)(8))(x^3)`