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3. Write the following expression in exponential form.

$\sqrt{{ab}}$ Show Solution

All this problem is asking us to do is basically use the definition of the radical notation and write this in exponential form instead of radical form.

$\require{bbox} \bbox[2pt,border:1px solid black]{{{{\left( {ab} \right)}^{\frac{1}{6}}}}}$

Be careful with parenthesis here! Recall that the only thing that gets the exponent is the term immediately to the left of the exponent. So, if we’d dropped parenthesis we’d get,

$a{b^{\frac{1}{6}}} = a\left( {{b^{\frac{1}{6}}}} \right) = a\,\,\sqrt{b}$

which is most definitely not what we started with. The only way to make sure that we understand that both the $$a$$ and the $$b$$ were under the radical is to use parenthesis as we did above.