Simplify the Expression: 3⁵ ÷ 3² Using Exponent Rules

Think of it this way: $\frac{3^5}{3^2} = \frac{3 \times 3 \times 3 \times 3 \times 3}{3 \times 3}$. The two 3's in the denominator cancel out two 3's in the numerator, leaving three 3's = $3^3$.

You still subtract! For example: $\frac{3^2}{3^5} = 3^{2-5} = 3^{-3} = \frac{1}{3^3}$. Negative exponents mean the result goes in the denominator.

No! The quotient rule only works when the bases are exactly the same. You can't simplify $\frac{2^3}{3^2}$ using this rule.

Using the exponent rule is much faster! $\frac{3^5}{3^2}$ means calculating $\frac{243}{9} = 27$, but $3^{5-2} = 3^3 = 27$ gets the same answer with less work.

The rule still works perfectly! $\frac{5^4}{5^1} = 5^{4-1} = 5^3$. Remember that any number to the first power is just itself, so $5^1 = 5$.