Here is the example we were given:
Given that $32√2 = 2^a$, find the value of $a$.
Here's the working out that was supplied:
$$32√2 = 2^5 \times 2^\frac{1}{2} = 2^\frac{11}{2}$$ $$a = \frac{11}{2}$$
I'm confused about how this:
$$2^5\times2^\frac{1}{2}$$
Was converted into this:
$$2^\frac{11}{2}$$
What happened?
Thank you.
For all $ x \in \mathbb{R}^+,\ y \in \mathbb{Q},\ z \in \mathbb{Q}$
$$ x^yx^z = x^{y+z}. $$
Therefore, $2^5\times2^{\small\frac{1}{2}} = 2^{5 +\small\frac{1}{2}} = 2^{\small\frac{10}{2} + {\small\frac{1}{2}}} = 2^{\small\frac{11}{2}}$