algebra precalculus - Anything to zero power equals one?

I am in Adv. Algebra 2 and I have a question. Firstly, would like to say I haven't taken algebra in a year due to geometry (stupid order they do but oh well) and I have a question understanding this: $(x+5)^{0}$. That would be $x^{0} + 5^{0}$ which then, wouldn't that be $1 + 1$ since anything that has a power of $0 = 1$? Maybe I misunderstood but that's what I got.

Answer

First, exponents do not distribute over addition. To start with the simplest example, $(a+b)^2=(a+b)(a+b)$. Applying the distributive rule, we see that this is the same as $a(a+b)+b(a+b) = a^2 + ab + ab + b^2$, which is different from $a^2+b^2$. This can be seen geometrically, too: A square built on a side of length $a+b$ has greater area than the square with side length $a$, combined with the square with side length $b$.

You can also see your result if you consider order of operations, and substitute an actual number for $x$. Let's consider $x=3$. Then we have:

$$(x+5)^0=(3+5)^0=8^0=1,$$

because Parentheses come before Exponents in PEMDAS.