Determin the value of \( r^{200} \) and \( s^{206} \) \( r=5 / 3 \)

Given that \( r = \frac{5}{3} \), we can substitute this value into the expressions \( r^{200} \) and \( s^{206} \) to find their values. Substitute \( r = \frac{5}{3} \) into the expression \( r^{200} \): \[ r^{200} = \left(\frac{5}{3}\right)^{200} \] Substitute \( r = \frac{5}{3} \) into the expression \( s^{206} \): \[ s^{206} = \left(\frac{5}{3}\right)^{206} \] Now, we can calculate the values of \( r^{200} \) and \( s^{206} \) using the given value of \( r \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{5}{3}\right)^{200}\) - step1: Use the properties of exponents: \(\frac{5^{200}}{3^{200}}\) Calculate or simplify the expression \( (5/3)^{206} \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{5}{3}\right)^{206}\) - step1: Use the properties of exponents: \(\frac{5^{206}}{3^{206}}\) The value of \( r^{200} \) is approximately \( 2.342879 \times 10^{44} \) and the value of \( s^{206} \) is approximately \( 5.021604 \times 10^{45} \).