If $\frac{5^7}{5^n}=5^{-2}$, what is the value of $n$?

Quotient rule: $\frac{5^7}{5^n}=5^{7-n}$, so $7-n=-2$. Moving terms across gives $n=7+2=9$. Doing $7-2$ instead produces the trap 5, and copying the minus sign from $5^{-2}$ straight onto the answer gives $-9$.