1. **State the problem:** Evaluate the expression $125^{-\frac{2}{3}}$. 2. **Recall the rule for negative and fractional exponents:** - A negative exponent means take the reciprocal: $a^{-n} = \frac{1}{a^n}$. - A fractional exponent means a root and a power: $a^{\frac{m}{n}} = \sqrt[n]{a^m}$. 3. **Apply the negative exponent rule:** $$125^{-\frac{2}{3}} = \frac{1}{125^{\frac{2}{3}}}$$ 4. **Evaluate the fractional exponent $125^{\frac{2}{3}}$:** - First find the cube root of 125: $\sqrt[3]{125} = 5$ because $5^3 = 125$. - Then square the result: $5^2 = 25$. So, $$125^{\frac{2}{3}} = 25$$ 5. **Substitute back:** $$125^{-\frac{2}{3}} = \frac{1}{25}$$ 6. **Final answer:** $$\boxed{\frac{1}{25}}$$