1. **State the problem:** Simplify the expression $$\frac{y^{10}}{y^3} \times \frac{y^4}{y^2}$$. 2. **Recall the exponent rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Simplify each fraction separately:** $$\frac{y^{10}}{y^3} = y^{10-3} = y^7$$ $$\frac{y^4}{y^2} = y^{4-2} = y^2$$ 4. **Multiply the simplified terms:** $$y^7 \times y^2 = y^{7+2} = y^9$$ 5. **Final answer:** $$y^9$$