Question

you can use properties of exponents to see why it makes sense that $3^0 = 1$.
how can you write the quotient as a single power?
$1 = \frac{3^1}{3^1}$
= ?
$3^{1+1}$
$3^{1-1}$
$3^{1\cdot1}$

Explanation:

Step1: Recall quotient of powers rule

For non-zero base $a$, $\frac{a^m}{a^n}=a^{m-n}$

Step2: Apply rule to $\frac{3^1}{3^1}$

Substitute $a=3$, $m=1$, $n=1$:
$\frac{3^1}{3^1}=3^{1-1}$

Step3: Simplify the exponent

$3^{1-1}=3^0$, which equals 1 as given.

Answer:

$3^{1-1}$