The index of the expression [tex]x^{\frac{2}{3} }[/tex] when it is rewritten as a radical is 2.
Given the expression [tex]x^{\frac{2}{3} }[/tex], to rewrite this as a radical expression, we first need to know what a radical expression is.
A radical expression is an expression of the form [tex]\sqrt[n]{x}[/tex].
So, [tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
So, the expression [tex]x^{\frac{2}{3} }[/tex] can be rewritten in the form
[tex]x^{\frac{2}{3} }[/tex] = [tex](\sqrt[3]{x} )^{2}[/tex] (Since from the laws of indices, [tex]x^{\frac{a}{n} } = (\sqrt[n]{x}) ^{a}[/tex])
So rewriting [tex]x^{\frac{2}{3} }[/tex] as a radical expression, we have
[tex]x^{\frac{2}{3} }[/tex] = [tex](\sqrt[3]{x} )^{2}[/tex]
Now, [tex](\sqrt[3]{x} )^{2}[/tex] is in radical form where [tex]\sqrt[3]{x}[/tex] is the radical.
Since [tex]\sqrt[3]{x}[/tex] is raised to the power of 2, the index of the expression [tex]x^{\frac{2}{3} }[/tex] when it is rewritten as a radical is 2.
So, the index of the expression [tex]x^{\frac{2}{3} }[/tex] when it is rewritten as a radical is 2.
Learn more about radical expressions here:
https://brainly.com/question/1601861
