\( \left. \begin{array} { l } { ( \$ 6 \times 1.07 ^ { 1 } ) / 1.20 ^ { 1 } = } \\ { ( \$ 6 \times 1.07 ^ { 2 } ) / 1.20 ^ { 2 } = } \\ { ( \$ 6 \times 1.07 ^ { 3 } ) / 1.20 ^ { 3 } = } \\ { ( \$ 6 \times 1.07 ^ { 4 } ) / 1.20 ^ { 4 } = } \end{array} \right. \)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6\times 1.07^{1}\right)}{1.2^{1}}\) - step1: Remove the parentheses: \(\frac{6\times 1.07^{1}}{1.2^{1}}\) - step2: Calculate: \(\frac{6\times \frac{107}{100}}{1.2^{1}}\) - step3: Calculate: \(\frac{6\times \frac{107}{100}}{\frac{6}{5}}\) - step4: Multiply the numbers: \(\frac{\frac{321}{50}}{\frac{6}{5}}\) - step5: Multiply by the reciprocal: \(\frac{321}{50}\times \frac{5}{6}\) - step6: Reduce the numbers: \(\frac{107}{10}\times \frac{1}{2}\) - step7: Multiply the fractions: \(\frac{107}{10\times 2}\) - step8: Multiply: \(\frac{107}{20}\) Calculate or simplify the expression \( (6 * 1.07 ^ 2) / 1.20 ^ 2 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6\times 1.07^{2}\right)}{1.2^{2}}\) - step1: Remove the parentheses: \(\frac{6\times 1.07^{2}}{1.2^{2}}\) - step2: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{2}}{1.2^{2}}\) - step3: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{2}}{\left(\frac{6}{5}\right)^{2}}\) - step4: Multiply the terms: \(\frac{\frac{34347}{5000}}{\left(\frac{6}{5}\right)^{2}}\) - step5: Evaluate the power: \(\frac{\frac{34347}{5000}}{\frac{36}{25}}\) - step6: Multiply by the reciprocal: \(\frac{34347}{5000}\times \frac{25}{36}\) - step7: Reduce the numbers: \(\frac{11449}{200}\times \frac{1}{12}\) - step8: Multiply the fractions: \(\frac{11449}{200\times 12}\) - step9: Multiply: \(\frac{11449}{2400}\) Calculate or simplify the expression \( (6 * 1.07 ^ 4) / 1.20 ^ 4 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6\times 1.07^{4}\right)}{1.2^{4}}\) - step1: Remove the parentheses: \(\frac{6\times 1.07^{4}}{1.2^{4}}\) - step2: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{4}}{1.2^{4}}\) - step3: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{4}}{\left(\frac{6}{5}\right)^{4}}\) - step4: Simplify: \(\frac{6\times \frac{107^{4}}{100^{4}}}{\left(\frac{6}{5}\right)^{4}}\) - step5: Evaluate the power: \(\frac{6\times \frac{107^{4}}{100^{4}}}{\frac{1296}{625}}\) - step6: Rewrite the expression: \(\frac{\frac{6\times 107^{4}}{100^{4}}}{\frac{1296}{625}}\) - step7: Multiply by the reciprocal: \(\frac{6\times 107^{4}}{100^{4}}\times \frac{625}{1296}\) - step8: Reduce the numbers: \(\frac{107^{4}}{100^{4}}\times \frac{625}{216}\) - step9: Rewrite the expression: \(\frac{107^{4}}{25^{4}\times 4^{4}}\times \frac{625}{216}\) - step10: Rewrite the expression: \(\frac{107^{4}}{25^{4}\times 4^{4}}\times \frac{25^{2}}{216}\) - step11: Reduce the numbers: \(\frac{107^{4}}{25^{2}\times 4^{4}}\times \frac{1}{216}\) - step12: Multiply the fractions: \(\frac{107^{4}}{400^{2}\times 216}\) - step13: Multiply: \(\frac{107^{4}}{216\times 400^{2}}\) Calculate or simplify the expression \( (6 * 1.07 ^ 3) / 1.20 ^ 3 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(6\times 1.07^{3}\right)}{1.2^{3}}\) - step1: Remove the parentheses: \(\frac{6\times 1.07^{3}}{1.2^{3}}\) - step2: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{3}}{1.2^{3}}\) - step3: Convert the expressions: \(\frac{6\left(\frac{107}{100}\right)^{3}}{\left(\frac{6}{5}\right)^{3}}\) - step4: Simplify: \(\frac{6\times \frac{107^{3}}{100^{3}}}{\left(\frac{6}{5}\right)^{3}}\) - step5: Evaluate the power: \(\frac{6\times \frac{107^{3}}{100^{3}}}{\frac{216}{125}}\) - step6: Rewrite the expression: \(\frac{\frac{6\times 107^{3}}{100^{3}}}{\frac{216}{125}}\) - step7: Multiply by the reciprocal: \(\frac{6\times 107^{3}}{100^{3}}\times \frac{125}{216}\) - step8: Reduce the numbers: \(\frac{107^{3}}{100^{3}}\times \frac{125}{36}\) - step9: Rewrite the expression: \(\frac{107^{3}}{25^{3}\times 4^{3}}\times \frac{125}{36}\) - step10: Rewrite the expression: \(\frac{107^{3}}{5^{6}\times 4^{3}}\times \frac{5^{3}}{36}\) - step11: Reduce the numbers: \(\frac{107^{3}}{5^{3}\times 4^{3}}\times \frac{1}{36}\) - step12: Multiply the fractions: \(\frac{107^{3}}{20^{3}\times 36}\) - step13: Multiply: \(\frac{107^{3}}{288000}\) Let's calculate each expression step by step: 1. **First Expression:** \[ \frac{6 \times 1.07^1}{1.20^1} = \frac{6 \times 1.07}{1.20} = \frac{6.42}{1.20} \approx 5.35 \] 2. **Second Expression:** \[ \frac{6 \times 1.07^2}{1.20^2} = \frac{6 \times 1.1449}{1.44} = \frac{6.8694}{1.44} \approx 4.77041 \] 3. **Third Expression:** \[ \frac{6 \times 1.07^3}{1.20^3} = \frac{6 \times 1.225043}{1.728} = \frac{7.350258}{1.728} \approx 4.253622 \] 4. **Fourth Expression:** \[ \frac{6 \times 1.07^4}{1.20^4} = \frac{6 \times 1.3107961}{2.0736} = \frac{7.8647766}{2.0736} \approx 3.792813 \] ### Summary of Results: - For \( \frac{6 \times 1.07^1}{1.20^1} \): **5.35** - For \( \frac{6 \times 1.07^2}{1.20^2} \): **4.77041** - For \( \frac{6 \times 1.07^3}{1.20^3} \): **4.253622** - For \( \frac{6 \times 1.07^4}{1.20^4} \): **3.792813**