1. **State the problem:** Simplify the expression $$(-192k)^{20}$$. 2. **Recall the rule for powers:** When raising a product to a power, raise each factor to that power: $$ (ab)^n = a^n b^n $$. 3. **Apply the rule:** $$ (-192k)^{20} = (-192)^{20} \times k^{20} $$ 4. **Consider the sign:** Since the exponent 20 is even, $$ (-192)^{20} = 192^{20} $$ because an even power of a negative number is positive. 5. **Final simplified form:** $$ (-192k)^{20} = 192^{20} k^{20} $$ This is the fully simplified expression. The number $$192^{20}$$ is very large and usually left in exponential form unless a numerical approximation is needed.