How do you express ##x^(4/3)## in simplest radical form?

You raise ##x## to the ##4^”th”## power, then take the cube root.

When dealing with , it’s always useful to remember that the exponent can be written as a product of an integer and of a fraction that has the numerator equal to 1.

In general, this looks like this

##a/b = a * 1/b##

This is important when dealing with fractional exponents because an exponent that takes the form ##1/b##, like in the above example, is equivalent to taking the ##b^”th”## root.

##x^(1/b) = root(b)(x)##

Since, for any ##x>0##, you have ##(x^a)^b = x^(a * b)##, you can write

##x^(4/3) = x^(4 * 1/3) = (x^4)^(1/3) = color(green)(root(3)(x^4))##

SImply put, you need to take the cube root from ##x## raised to the ##4^”th”## power.

Of course, you can also write

##x^(4/3) = x^(1/3*4) = (x^(1/3))^4 = color(green)((root(3)(x))^4##