1. **State the problem:** Simplify the expression by adding like terms: $$6x^2y^0 + 5x^2 + \frac{3x^3 y}{xy}$$ 2. **Recall important rules:** - Any variable raised to the zero power equals 1, so $y^0 = 1$. - When dividing powers with the same base, subtract the exponents: $$\frac{x^a}{x^b} = x^{a-b}$$ - Like terms have the same variables raised to the same powers. 3. **Simplify each term:** - Since $y^0 = 1$, rewrite the first term: $$6x^2y^0 = 6x^2 \times 1 = 6x^2$$ - The second term is $5x^2$. - Simplify the fraction: $$\frac{3x^3 y}{xy} = 3 \times \frac{x^3}{x^1} \times \frac{y^1}{y^1} = 3x^{3-1}y^{1-1} = 3x^2 y^0 = 3x^2 \times 1 = 3x^2$$ 4. **Combine like terms:** All terms are like terms with $x^2$, so add their coefficients: $$6x^2 + 5x^2 + 3x^2 = (6 + 5 + 3)x^2 = 14x^2$$ 5. **Final answer:** $$\boxed{14x^2}$$