How do you write $x^{\frac{2}{3}}$ $x^(2/3)$ in radical form?

Question

196212 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-09T14:03:41

See a solution process below:

First, we can rewrite the term as:

$x^{2 \times \frac{1}{3}}$ $x^(2 xx 1/3)$

Next, we can use this rule of exponents to rewrite the term again:

$x^{a \times b} = {(x^{a})}^{b}$ $x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)$

$x^{2 \times \frac{1}{3}} \Rightarrow {(x^{2})}^{\frac{1}{3}}$ $x^(color(red)(2) xx color(blue)(1/3)) => (x^color(red)(2))^color(blue)(1/3)$

Now, we can use this rule to write the term as an radical:

$x^{\frac{1}{n}} = \sqrt[n]{x}$ $x^(1/color(red)(n)) = root(color(red)(n))(x)$

${(x^{2})}^{\frac{1}{3}} = \sqrt[3]{(x^{2})}$ $(x^2)^(1/color(red)(3)) = root(color(red)(3))((x^2))$

How do you write x23x^(2/3) in radical form?