1. **State the problem:** Evaluate the expression $$\left(\frac{25}{36}\right)^{\frac{3}{2}}$$ where the exponent is a fractional power. 2. **Recall the rule for fractional exponents:** For any positive number $a$ and rational exponent $\frac{m}{n}$, we have $$a^{\frac{m}{n}} = \left(a^{\frac{1}{n}}\right)^m = \sqrt[n]{a^m}$$ This means we can either take the $n$th root first and then raise to the $m$th power, or vice versa. 3. **Apply the first form:** Since both 25 and 36 are perfect squares, it is easier to take the square root first: $$\left(\frac{25}{36}\right)^{\frac{3}{2}} = \left(\left(\frac{25}{36}\right)^{\frac{1}{2}}\right)^3 = \left(\sqrt{\frac{25}{36}}\right)^3$$ 4. **Calculate the square root:** $$\sqrt{\frac{25}{36}} = \frac{\sqrt{25}}{\sqrt{36}} = \frac{5}{6}$$ 5. **Raise the result to the 3rd power:** $$\left(\frac{5}{6}\right)^3 = \frac{5^3}{6^3} = \frac{125}{216}$$ 6. **Final answer:** $$\left(\frac{25}{36}\right)^{\frac{3}{2}} = \frac{125}{216}$$ This means the power and root evaluation yields the fraction $\frac{125}{216}$ as the final result.