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Section 1.3 : Radicals

4. Write the following expression in exponential form.

\[\sqrt {{w^2}{v^3}} \] 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.

\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\left( {{w^2}{v^3}} \right)}^{\frac{1}{2}}}}}\]

Recall that when no index is written on the radical it is assumed to be 2.

Also, be careful with parenthesis here! Recall that the only thing that gets the exponent is the term immediately to the left of the exponent and so we need parenthesis on the whole thing to make sure that we understand that both terms were under the root.