2. a. \( \left(\frac{1}{2}\right)^{-1} \) b. \( \left(\frac{2}{3}\right)^{-1} \) c. \( \left(\frac{3}{5}\right)^{-1} \) d. \( \left(\frac{1}{3}\right)^{-2} \) e. \( \frac{1}{2^{-2}} \) f. \( \left(\frac{3}{4}\right)^{-3} \)

Calculate the value by following steps: - step0: Calculate: \(\frac{3}{4}-3\) - step1: Reduce fractions to a common denominator: \(\frac{3}{4}-\frac{3\times 4}{4}\) - step2: Transform the expression: \(\frac{3-3\times 4}{4}\) - step3: Multiply the numbers: \(\frac{3-12}{4}\) - step4: Subtract the numbers: \(\frac{-9}{4}\) - step5: Rewrite the fraction: \(-\frac{9}{4}\) Calculate or simplify the expression \( (1/2)^-1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{1}{2}-1\) - step1: Reduce fractions to a common denominator: \(\frac{1}{2}-\frac{2}{2}\) - step2: Transform the expression: \(\frac{1-2}{2}\) - step3: Subtract the numbers: \(\frac{-1}{2}\) - step4: Rewrite the fraction: \(-\frac{1}{2}\) Calculate or simplify the expression \( (3/5)^-1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{3}{5}-1\) - step1: Reduce fractions to a common denominator: \(\frac{3}{5}-\frac{5}{5}\) - step2: Transform the expression: \(\frac{3-5}{5}\) - step3: Subtract the numbers: \(\frac{-2}{5}\) - step4: Rewrite the fraction: \(-\frac{2}{5}\) Calculate or simplify the expression \( (2/3)^-1 \). Calculate the value by following steps: - step0: Calculate: \(\frac{2}{3}-1\) - step1: Reduce fractions to a common denominator: \(\frac{2}{3}-\frac{3}{3}\) - step2: Transform the expression: \(\frac{2-3}{3}\) - step3: Subtract the numbers: \(\frac{-1}{3}\) - step4: Rewrite the fraction: \(-\frac{1}{3}\) Calculate or simplify the expression \( (1/3)^-2 \). Calculate the value by following steps: - step0: Calculate: \(\frac{1}{3}-2\) - step1: Reduce fractions to a common denominator: \(\frac{1}{3}-\frac{2\times 3}{3}\) - step2: Transform the expression: \(\frac{1-2\times 3}{3}\) - step3: Multiply the numbers: \(\frac{1-6}{3}\) - step4: Subtract the numbers: \(\frac{-5}{3}\) - step5: Rewrite the fraction: \(-\frac{5}{3}\) Let's solve each part step by step: ### a. \( \left(\frac{1}{2}\right)^{-1} \) The negative exponent indicates that we take the reciprocal of the base: \[ \left(\frac{1}{2}\right)^{-1} = \frac{1}{\frac{1}{2}} = 2 \] ### b. \( \left(\frac{2}{3}\right)^{-1} \) Similarly, we take the reciprocal: \[ \left(\frac{2}{3}\right)^{-1} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5 \] ### c. \( \left(\frac{3}{5}\right)^{-1} \) Taking the reciprocal again: \[ \left(\frac{3}{5}\right)^{-1} = \frac{1}{\frac{3}{5}} = \frac{5}{3} \approx 1.6667 \] ### d. \( \left(\frac{1}{3}\right)^{-2} \) For a negative exponent squared, we first take the reciprocal and then square it: \[ \left(\frac{1}{3}\right)^{-2} = \left(\frac{3}{1}\right)^{2} = 3^2 = 9 \] ### e. \( \frac{1}{2^{-2}} \) Calculating \( 2^{-2} \): \[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \] Thus, \[ \frac{1}{2^{-2}} = \frac{1}{\frac{1}{4}} = 4 \] ### f. \( \left(\frac{3}{4}\right)^{-3} \) Taking the reciprocal and cubing: \[ \left(\frac{3}{4}\right)^{-3} = \left(\frac{4}{3}\right)^{3} = \frac{4^3}{3^3} = \frac{64}{27} \approx 2.3704 \] ### Summary of Results: - a. \( 2 \) - b. \( 1.5 \) - c. \( \frac{5}{3} \) or approximately \( 1.6667 \) - d. \( 9 \) - e. \( 4 \) - f. \( \frac{64}{27} \) or approximately \( 2.3704 \)