would you please explain #12 in test 5, section 3.


Yeah, this one is trickier than it looks. I think most people get turned around on it because they try to get out of fractional exponent notation too early, and then they get stuck. It’s a LOT easier, in my opinion, to do a little manipulation in exponent form before you jump to radicals. In this case, that means making a 9=3^2 substitution, which will allow you to reduce the fraction.


Remember than when you raise a power to a power, you multiply those powers. So:


Now you can convert way more comfortably to radical notation. Remember, with fractional exponents, the numerator (top number in the fraction) is the power and the denominator (bottom number in the fraction) is the root.

    \begin{align*}&3^{3/2}\\=&\sqrt{3^3}\\=&\sqrt{3\times 3\times 3}\\=&3\sqrt{3}\end{align*}

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