1. **State the problem:** Given two functions $p(x) = ab^x$ and $r(x) = ca^x$, find the expression for $p(x) \cdot r(x)$. 2. **Recall the formula for multiplying exponential functions:** When multiplying terms with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$ 3. **Multiply the given functions:** $$p(x) \cdot r(x) = (ab^x)(ca^x)$$ 4. **Rearrange the terms:** $$= a \cdot c \cdot b^x \cdot a^x$$ 5. **Combine the exponential terms:** Since $b^x$ and $a^x$ have different bases, multiply them as: $$b^x \cdot a^x = (ba)^x$$ 6. **Write the final expression:** $$p(x) \cdot r(x) = ac(ba)^x$$ 7. **Match with the answer choices:** The expression matches option c: $$ac(bd)^x$$ if we consider $d = a$ (assuming a typo in the problem or $d$ is $a$). Since the problem uses $a$ and $b$ only, the correct form is $$ac(ba)^x$$ which corresponds to option c with $d = a$. **Final answer:** $$p(x) \cdot r(x) = ac(bd)^x$$