\( 6000(1.03)^{2(13)} \approx \square \) (Round to two decimal places as needed.)

Calculate or simplify the expression \( 6000(1.03)^{2(13)} \). Calculate the value by following steps: - step0: Calculate: \(6000\times 1.03^{2\times 13}\) - step1: Multiply the numbers: \(6000\times 1.03^{26}\) - step2: Convert the expressions: \(6000\left(\frac{103}{100}\right)^{26}\) - step3: Simplify: \(6000\times \frac{103^{26}}{100^{26}}\) - step4: Rewrite the expression: \(1000\times 6\times \frac{103^{26}}{100^{26}}\) - step5: Rewrite the expression: \(10^{3}\times 6\times \frac{103^{26}}{10^{52}}\) - step6: Reduce the numbers: \(6\times \frac{103^{26}}{10^{49}}\) - step7: Rewrite the expression: \(2\times 3\times \frac{103^{26}}{10^{49}}\) - step8: Rewrite the expression: \(2\times 3\times \frac{103^{26}}{2^{49}\times 5^{49}}\) - step9: Reduce the numbers: \(3\times \frac{103^{26}}{2^{48}\times 5^{49}}\) - step10: Multiply the fractions: \(\frac{3\times 103^{26}}{2^{48}\times 5^{49}}\) The approximate value of \(6000(1.03)^{2(13)}\) is approximately 12939.55 when rounded to two decimal places.