Simplify the following: 1. a. \( 5^{-1} \) b. \( -6^{-1} \) c. \( (-8)^{-1} \) d. \( 3^{-2} \) e. \( (-2)^{-3} \) f. \( -4^{-3} \)

Calculate the value by following steps: - step0: Calculate: \(3^{-2}\) - step1: Express with a positive exponent: \(\frac{1}{3^{2}}\) - step2: Evaluate the power: \(\frac{1}{9}\) Calculate or simplify the expression \( (-8)^{-1} \). Calculate the value by following steps: - step0: Calculate: \(\left(-8\right)^{-1}\) - step1: Express with a positive exponent: \(\frac{1}{-8}\) - step2: Rewrite the fraction: \(-\frac{1}{8}\) Calculate or simplify the expression \( -4^{-3} \). Calculate the value by following steps: - step0: Calculate: \(-4^{-3}\) - step1: Express with a positive exponent: \(\frac{-1}{4^{3}}\) - step2: Evaluate the power: \(\frac{-1}{64}\) - step3: Rewrite the fraction: \(-\frac{1}{64}\) Calculate or simplify the expression \( (-2)^{-3} \). Calculate the value by following steps: - step0: Calculate: \(\left(-2\right)^{-3}\) - step1: Express with a positive exponent: \(\frac{1}{\left(-2\right)^{3}}\) - step2: Evaluate the power: \(\frac{1}{-8}\) - step3: Rewrite the fraction: \(-\frac{1}{8}\) Calculate or simplify the expression \( 5^{-1} \). Calculate the value by following steps: - step0: Calculate: \(5^{-1}\) - step1: Express with a positive exponent: \(\frac{1}{5}\) Calculate or simplify the expression \( -6^{-1} \). Calculate the value by following steps: - step0: Calculate: \(-6^{-1}\) - step1: Express with a positive exponent: \(\frac{-1}{6}\) - step2: Rewrite the fraction: \(-\frac{1}{6}\) Here are the simplified results for each expression: 1. a. \( 5^{-1} = \frac{1}{5} \) or \( 0.2 \) 1. b. \( -6^{-1} = -\frac{1}{6} \) or \( -0.1\dot{6} \) 1. c. \( (-8)^{-1} = -\frac{1}{8} \) or \( -0.125 \) 1. d. \( 3^{-2} = \frac{1}{9} \) or \( 0.\dot{1} \) 1. e. \( (-2)^{-3} = -\frac{1}{8} \) or \( -0.125 \) 1. f. \( -4^{-3} = -\frac{1}{64} \) or \( -0.015625 \) You can choose the format that best suits your needs!