1. **State the problem:** Simplify the expression $\left(s^3 t^5\right)^4$ and write it as a single power. 2. **Recall the power of a product rule:** When raising a product to a power, apply the exponent to each factor inside the parentheses: $$\left(ab\right)^n = a^n b^n$$ 3. **Apply the rule:** $$\left(s^3 t^5\right)^4 = \left(s^3\right)^4 \left(t^5\right)^4$$ 4. **Use the power of a power rule:** $$\left(a^m\right)^n = a^{m \times n}$$ 5. **Calculate each term:** $$\left(s^3\right)^4 = s^{3 \times 4} = s^{12}$$ and $$\left(t^5\right)^4 = t^{5 \times 4} = t^{20}$$ 6. **Write the final simplified expression:** $$s^{12} t^{20}$$ **Answer:** $s^{12} t^{20}$