1. Evaluate each power without using a calculator. **a)** $16^{1/2}$ means the square root of 16. $$16^{1/2} = \sqrt{16} = 4$$ **b)** $36^{1/2}$ means the square root of 36. $$36^{1/2} = \sqrt{36} = 6$$ **c)** $64^{1/3}$ means the cube root of 64. $$64^{1/3} = \sqrt[3]{64} = 4$$ **d)** $32^{1/5}$ means the fifth root of 32. $$32^{1/5} = \sqrt[5]{32} = 2$$ **e)** $(-27)^{1/3}$ means the cube root of -27. $$(-27)^{1/3} = \sqrt[3]{-27} = -3$$ **f)** $(-1000)^{1/3}$ means the cube root of -1000. $$(-1000)^{1/3} = \sqrt[3]{-1000} = -10$$ --- **Summary:** The key rule is that $a^{1/n} = \sqrt[n]{a}$, the $n$th root of $a$. For odd roots, negative numbers are allowed and the root is negative. Final answers: **a)** 4 **b)** 6 **c)** 4 **d)** 2 **e)** -3 **f)** -10