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

Jul 24, 2015

You raise $x$ to the ${4}^{\text{th}}$ power, then take the cube root.

#### Explanation:

When dealing with fractional exponents, 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

$\frac{a}{b} = a \cdot \frac{1}{b}$

This is important when dealing with fractional exponents because an exponent that takes the form $\frac{1}{b}$, like in the above example, is equivalent to taking the ${b}^{\text{th}}$ root.

${x}^{\frac{1}{b}} = \sqrt[b]{x}$

Since, for any $x > 0$, you have ${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$, you can write

${x}^{\frac{4}{3}} = {x}^{4 \cdot \frac{1}{3}} = {\left({x}^{4}\right)}^{\frac{1}{3}} = \textcolor{g r e e n}{\sqrt[3]{{x}^{4}}}$

SImply put, you need to take the cube root from $x$ raised to the ${4}^{\text{th}}$ power.

Of course, you can also write

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