1. **State the problem:** Simplify the expression $2m^4 \times 5m^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the exponents: $a^x \times a^y = a^{x+y}$. 3. **Apply the rule to the expression:** $$2m^4 \times 5m^2 = (2 \times 5)(m^{4+2})$$ 4. **Simplify the coefficients and exponents:** $$= 10m^6$$ 5. **Final answer:** The simplified form of $2m^4 \times 5m^2$ is $10m^6$.