## Algebra 1

$\frac{1}{a}$
We start with the given expression: $a^2b^0(a^{-3})$ The zero as an exponent rule states that for every nonzero number $a$, $a^0=1$. Since anything multiplied by $1$ is itself, we can disregard the $b^0$ term: $a^2a^{-3}$ To multiply powers with the same base, we add the exponents: $a^{2+(-3)}=a^{-1}$ The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{1}{a^1}=\frac{1}{a}$