Solve 5^6 ÷ 5^4: Division of Powers with Same Base

The quotient rule says $\frac{a^m}{a^n} = a^{m-n}$. This comes from canceling out common factors. When you have $\frac{5^6}{5^4}$, you're canceling four 5's from top and bottom, leaving $5^2$.

You still subtract! For example, $\frac{5^3}{5^7} = 5^{3-7} = 5^{-4}$. The negative exponent means one over that positive power: $\frac{1}{5^4}$.

Yes! $\frac{5^6}{5^4} = \frac{5 \times 5 \times 5 \times 5 \times 5 \times 5}{5 \times 5 \times 5 \times 5}$. Cancel four 5's from top and bottom, leaving $5 \times 5 = 5^2$. This is exactly what the quotient rule does!

Absolutely! The quotient rule $\frac{a^m}{a^n} = a^{m-n}$ works for any base. Try $\frac{3^8}{3^5} = 3^{8-5} = 3^3$ or $\frac{x^{10}}{x^7} = x^3$.

For $5^2 = 25$, you can verify by thinking: $5^6 = 15625$ and $5^4 = 625$. Since $625 \times 25 = 15625$, our answer $5^2 = 25$ is correct!