1. **State the problem:** We have a function $h(x) = a^x + b$ where $a$ and $b$ are positive constants. The graph passes through points $(0, 10)$ and $\left(-2, \frac{325}{36}\right)$. We need to find the value of $ab$. 2. **Use the points to form equations:** - At $x=0$, $h(0) = a^0 + b = 1 + b = 10$. - So, $b = 10 - 1 = 9$. 3. **Use the second point:** - At $x = -2$, $h(-2) = a^{-2} + b = \frac{325}{36}$. - Substitute $b=9$: $$a^{-2} + 9 = \frac{325}{36}$$ 4. **Solve for $a^{-2}$:** $$a^{-2} = \frac{325}{36} - 9 = \frac{325}{36} - \frac{324}{36} = \frac{1}{36}$$ 5. **Rewrite $a^{-2}$:** $$a^{-2} = \frac{1}{a^2} = \frac{1}{36} \implies a^2 = 36$$ 6. **Find $a$:** - Since $a$ is positive, $a = 6$. 7. **Calculate $ab$:** $$ab = 6 \times 9 = 54$$ **Final answer:** $ab = 54$. This corresponds to option C.