Question

Express (81^1/2) ^5 in simplest radical form

Answer 1

$9^5$

1) Let's simplify this expression, making use of the properties of the exponents.

2) So we can write it out:

$\begin{gathered} (a^b)^c=a^{bc} \\ (81^{\frac{1}{2}})^5=((9^2)^{\frac{1}{2}})^5=(9^{\frac{2}{2}})^5=9^5 \end{gathered}$

Note that we rewrote 81 as power and then applied the property of the exponents