1. **Problem:** Simplify $9^{3/2}$. 2. **Formula and rules:** For any positive number $a$ and rational exponent $m/n$, we use the rule: $$a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m$$ This means we can take the $n$th root first, then raise to the $m$th power, or vice versa. 3. **Apply to $9^{3/2}$:** Since the denominator is 2, this is a square root, and the numerator is 3. $$9^{3/2} = (9^{1/2})^3 = (\sqrt{9})^3$$ 4. **Calculate the square root:** $$\sqrt{9} = 3$$ 5. **Raise to the power 3:** $$3^3 = 27$$ 6. **Final answer:** $$9^{3/2} = 27$$ This matches the simplification steps shown in the handwritten graph where the square root of 9 is taken first, then cubed.