Simplify the Expression: (a^xy)/(a^3xy) - a^2xy Using Power Rules

These terms have different exponents (-2xy and +2xy), so they're not like terms. You can only combine terms when they have identical variable parts and exponents.

A negative exponent means reciprocal! So $a^{-2xy} = \frac{1}{a^{2xy}}$. However, in this problem we keep it in negative exponent form.

When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$. So $\frac{a^{xy}}{a^{3xy}} = a^{xy-3xy} = a^{-2xy}$.

No! There's a subtraction sign between them, not addition. You can only cancel terms when they're being added and have opposite signs.

Yes! You could write it as $\frac{1}{a^{2xy}} - a^{2xy}$, but the form $a^{-2xy} - a^{2xy}$ is more compact and commonly preferred.