Question

Give an example of an expression with a rational exponent and explain how to convert it into radical form.

Answer 1

The general rule is: \(\tiny \\[0.5em]\)
\(\color{black}{\large \displaystyle x^{ \color{red}{ a}/\color{blue}{b}}=\sqrt[\color{blue}{b}]{x^{\color{red}{ a}}} }\)

Answer 2

For example, \(\tiny \\[0.8em]\)
\(\color{black}{\large \displaystyle x^{4/7}=\sqrt[7]{\,x^4\,} }\)

Answer 3

Or, another example,
\(\color{black}{\large \displaystyle x^{1/2}=\sqrt[2]{x^1}=\sqrt{x}}\)


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Remark: \(\color{black}{ \sqrt[2]{f(x)}}\) is the same thing
as \(\color{black}{ \sqrt{f(x)}}\), and \(\color{black}{ \displaystyle x^1=x}\), this is how
I wrote my 3rd (final) step.
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Answer 4

It doesn't have to be \(x\), it can be a number as well.

For example, \(\tiny \\[0.8em]\)
\(\color{black}{\large \displaystyle 7^{2/3}=\sqrt[3]{\,7^2\,} }\).

Answer 5

I was wondering what they mean in politics by "Radical Muslims" ?
Is it \(\color{black}{\large \displaystyle \sqrt{\normalsize\rm Muslims}}\) ?

Answer 6

Just kidding ...
Anyway, do you understand the rule?
Do you have any questions?