1. State the problem: Solve for $d$ in the equation $$(17^3)^d = 17^{12}$$. 2. Use the power of a power rule: When raising an exponential expression to another power, multiply the exponents. $$ (a^m)^n = a^{mn} $$ 3. Apply this to the left side: $$ (17^3)^d = 17^{3d} $$ 4. Set the exponents equal since the bases are the same and the equation holds: $$ 3d = 12 $$ 5. Solve for $d$: $$ d = \frac{12}{3} = 4 $$ Answer: $d = 4$.