Simplify the Expression: Finding 9^9 ÷ 9^3 Using Power Rules

Think of it as canceling out common factors! $9^9$ means nine 9's multiplied together, and $9^3$ means three 9's. When we divide, we cancel three 9's from the top, leaving six 9's = $9^6$.

You still subtract! For example, $\frac{9^3}{9^9} = 9^{3-9} = 9^{-6}$. The negative exponent means one over that positive power: $\frac{1}{9^6}$.

No! The bases must be exactly the same. You can't simplify $\frac{9^4}{3^2}$ using this rule. However, since $9 = 3^2$, you could rewrite it first!

Use the multiplication rule backwards! If $\frac{9^9}{9^3} = 9^6$ is correct, then $9^6 \times 9^3$ should equal $9^9$. Since 6 + 3 = 9, it works!

Handle the coefficients separately! For $\frac{6 \cdot 9^9}{2 \cdot 9^3}$, you get $\frac{6}{2} \cdot \frac{9^9}{9^3} = 3 \cdot 9^6$. Deal with numbers and powers as separate parts.