How do you solve Practice test 6 Section 3 Number 16?

Remember that, for questions like this one, you only need to find one solution, not all solutions. Therefore, go for the simplest one you can!

Think of powers you know that land on 16. The first one that comes to mind for me is 4^2=16. The only restriction the question places on a and b is that they must both be positive integers, so let’s pick numbers that will make the given equation the same as 4^2=16.

Obviously we can make the base a = 4. How do we make the exponent equal to 2? Well, \dfrac{8}{4}=2, so let’s say b = 8.

    \begin{align*}a^\frac{b}{4}&=16\\\\4^\frac{8}{4}&=16\\\\4^2&=16\end{align*}

So there you go: 8 is one valid answer. For each of the other answers (1, 2, 4, 8, and 16 are all valid) there’s an exponential expression that works. While I find some of the following routes a little less obvious, all are valid:

    \begin{align*}2^4=16\qquad\Longrightarrow\qquad b=16\end{align*}

    \begin{align*}16^1=16\qquad\Longrightarrow\qquad b=4\end{align*}

    \begin{align*}256^\frac{1}{2}=16\qquad\Longrightarrow\qquad b=2\end{align*}

    \begin{align*}65536^\frac{1}{4}=16\qquad\Longrightarrow\qquad b=1\end{align*}