7^15:7^12/7^2

To solve the expression \( \frac{7^{15} \cdot 7^{12}}{7^2} \), you can use the laws of exponents.

1. First, use the property of exponents \( a^m \cdot a^n = a^{m+n} \) for the numerator: \[ 7^{15} \cdot 7^{12} = 7^{15 + 12} = 7^{27} \]

2. Now, replace the numerator in the original expression: \[ \frac{7^{27}}{7^2} \]

3. Next, apply the property \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{7^{27}}{7^2} = 7^{27 - 2} = 7^{25} \]

Thus, the final answer is: \[ 7^{25} \]