1. **Problem statement:** Evaluate the expressions: a) $5^{-3}$ b) $\left(\sqrt[3]{216}\right)^2$ 2. **Formula and rules:** - For negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$. - The cube root $\sqrt[3]{x}$ is the number which when cubed gives $x$. 3. **Evaluate a) $5^{-3}$:** $$5^{-3} = \frac{1}{5^3}$$ $$= \frac{1}{125}$$ 4. **Evaluate b) $\left(\sqrt[3]{216}\right)^2$:** First find $\sqrt[3]{216}$: $$\sqrt[3]{216} = 6 \quad \text{since } 6^3 = 216$$ Now square it: $$6^2 = 36$$ **Final answers:** - a) $5^{-3} = \frac{1}{125}$ - b) $\left(\sqrt[3]{216}\right)^2 = 36$