1. **State the problem:** Simplify the expression $\frac{x^2}{7} \times \frac{x^4}{7}$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the exponents: $$x^a \times x^b = x^{a+b}$$ 3. **Multiply the coefficients:** The coefficients are $\frac{1}{7}$ and $\frac{1}{7}$, so multiply them: $$\frac{1}{7} \times \frac{1}{7} = \frac{1}{49}$$ 4. **Add the exponents of $x$:** $$2 + 4 = 6$$ 5. **Write the simplified expression:** $$\frac{1}{49} x^6 = \frac{x^6}{49}$$ **Final answer:** $$\frac{x^6}{49}$$