1. Express $8^{-1}$ using positive indices. 2. Express $c^{-5}$ using positive indices. 3. Express $\frac{5}{l^{-6}}$ using positive indices. 4. Express $s^{-2} t^{-3}$ using positive indices. 5. Express $\frac{7 a^{-3}}{b^{-5}}$ using positive indices. 6. Express $(c^{-4} d^{-5})^2$ using positive indices. --- **Step 1: Understanding negative indices rule** The rule for negative indices is: $$a^{-n} = \frac{1}{a^n}$$ This means a negative exponent indicates the reciprocal of the base raised to the positive exponent. --- **Step 2: Apply the rule to each expression** 1. $8^{-1} = \frac{1}{8^1} = \frac{1}{8}$ 2. $c^{-5} = \frac{1}{c^5}$ 3. $\frac{5}{l^{-6}} = 5 \times l^{6}$ because dividing by $l^{-6}$ is multiplying by $l^6$ 4. $s^{-2} t^{-3} = \frac{1}{s^2} \times \frac{1}{t^3} = \frac{1}{s^2 t^3}$ 5. $\frac{7 a^{-3}}{b^{-5}} = 7 \times \frac{1}{a^3} \times b^5 = 7 b^5 \times \frac{1}{a^3} = \frac{7 b^5}{a^3}$ 6. $(c^{-4} d^{-5})^2 = c^{-8} d^{-10} = \frac{1}{c^8} \times \frac{1}{d^{10}} = \frac{1}{c^8 d^{10}}$ --- **Final answers:** 1. $\frac{1}{8}$ 2. $\frac{1}{c^5}$ 3. $5 l^6$ 4. $\frac{1}{s^2 t^3}$ 5. $\frac{7 b^5}{a^3}$ 6. $\frac{1}{c^8 d^{10}}$