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Section 1.2 : Rational Exponents

1. Evaluate the following expression and write the answer as a single number without exponents.

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, \[{b^{\frac{1}{n}}} = ?\hspace{0.25in}\hspace{0.25in}{\mbox{is equivalent to}}\hspace{0.25in}{?^n} = b\]
Show Solution

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.