1. We are given the equation $(2x^3)^a = bx^{12}$ and need to find the values of $a$ and $b$. 2. First, apply the power to both the coefficient and variable inside the parentheses: $$(2x^3)^a = 2^a (x^3)^a = 2^a x^{3a}$$ 3. The equation becomes: $$2^a x^{3a} = b x^{12}$$ 4. For the expressions to be equal for all $x$, the exponents of $x$ must be equal: $$3a = 12$$ Solving for $a$: $$a = \frac{12}{3} = 4$$ 5. Now substitute $a=4$ back into the coefficient equality: $$2^a = b \Rightarrow b = 2^4 = 16$$ 6. So the values are: $$a=4$$ $$b=16$$