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

Answer 1

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

It's helpful to keep in mind that an exponent can be expressed as the product of an integer and a fraction with a numerator of 1. This is especially helpful when working with fractional exponents.

This appears like this in general.

#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.

Naturally, you can write as well.

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

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eli Assouline

To express (x^\frac{4}{3}) in simplest radical form, you can rewrite it as (\sqrt[3]{x^4}).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.