Complete the Expression: Finding the Equal Value of 3^(x-y)

When you subtract exponents, you're essentially dividing powers! The law $a^{m-n} = \frac{a^m}{a^n}$ shows this relationship clearly. Think of it as: "x minus y" becomes "x divided by y" in exponential form.

Use this trick: the first term in the subtraction goes on top! In $3^{x-y}$, x comes first, so $3^x$ goes in the numerator. The second term (y) gives us $3^y$ in the denominator.

No, they're completely different! $3^{x-y}$ means subtract the exponents, while $(3^x)^y$ means multiply them: $(3^x)^y = 3^{xy}$. Don't confuse subtraction with power-to-power rules!

This rule works for any base! Whether it's $2^{a-b}$, $x^{m-n}$, or $10^{p-q}$, they all follow the same pattern: $\text{base}^{\text{first} - \text{second}} = \frac{\text{base}^{\text{first}}}{\text{base}^{\text{second}}}$.

That's perfectly fine! If x < y, then $3^{x-y}$ will have a negative exponent, which means $\frac{3^x}{3^y}$ will be a fraction less than 1. The rule still works the same way!