To simplify \( 12^{87} ÷ 12^{25} \), we can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).
Applying this to our expression:
\[ 12^{87} ÷ 12^{25} = 12^{87 - 25} \]
Now, we compute \( 87 - 25 \):
\[ 87 - 25 = 62 \]
Thus, we have:
\[ 12^{87} ÷ 12^{25} = 12^{62} \]
So, the simplified form is:
\[ \boxed{12^{62}} \]