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Section 1.2 : Rational Exponents
1. Evaluate the following expression and write the answer as a single number without exponents.
\[{36^{\frac{1}{2}}}\]
Hint : Recall that \({b^{\frac{1}{n}}}\) is really asking what number did we raise to the \(n\) to get \(b\). Or in other words,
\[{b^{\frac{1}{n}}} = ?\hspace{0.25in}\hspace{0.25in}{\mbox{is equivalent to}}\hspace{0.25in}{?^n} = b\]
For this problem we know that \({6^2} = 36\) and so we also know that,
\[{36^{\frac{1}{2}}} = \require{bbox} \bbox[2pt,border:1px solid black]{6}\]Note that if you aren’t sure of the answer to these kinds of problems all you really need to do is set up
\[{?^2} = 36\]and start trying integers until you get the one you need.