1. **State the problem:** Simplify the expression $ (16x^3) \times 3x^3 $. 2. **Recall the multiplication rules:** When multiplying coefficients (numbers), multiply them directly. When multiplying powers with the same base, add the exponents: $$ a^m \times a^n = a^{m+n} $$ 3. **Multiply the coefficients:** $$ 16 \times 3 = 48 $$ 4. **Multiply the powers of $x$:** $$ x^3 \times x^3 = x^{3+3} = x^6 $$ 5. **Combine the results:** $$ (16x^3) \times 3x^3 = 48x^6 $$ **Final answer:** $$ \boxed{48x^6} $$