1. **State the problem:** We want to find the resulting exponent on $y$ in the expression $$\left(\frac{x^m}{y^n}\right)^a$$ when $m=7$, $n=6$, and $a=6$. 2. **Recall the exponent rule:** When raising a quotient to a power, apply the power to both numerator and denominator: $$\left(\frac{x^m}{y^n}\right)^a = \frac{x^{m \cdot a}}{y^{n \cdot a}}$$ 3. **Apply the values:** $$\frac{x^{7 \cdot 6}}{y^{6 \cdot 6}} = \frac{x^{42}}{y^{36}}$$ 4. **Result:** The exponent on $y$ is $36$. Therefore, the resulting exponent on $y$ is **36**.