If a + b + c = 2024 and 1/a + 1/b + 1/c = 1/2024 find 1/a²⁰²⁵ + 1/b²⁰²⁵ +1/c²⁰²⁵ ----------------------------------------------------- Just pick one of the variables to be 2024 and the other two to be any opposite non-zero numbers, say, k and -k Say a = 2024, b = k, c = -k Then 2014 + k - k = 2024 and 1/2024 + 1/k + 1/(-k) = 1/2024 Then 1/2024²⁰²⁵ + 1/k²⁰²⁵ - 1/k²⁰²⁵ = 1/2024²⁰²⁵ If you want a decimal approximation and you put it in your calculator like it is you'll get an overflow because no ordinary device can handle numbers as large as 2024²⁰²⁵ or as small as 1/2024²⁰²⁵ So here's what you do to get it in scientific notation: Use base 10 logs: n = 2024^(-2025) log(n) = log(2025^(-2025) log(n) = -2025*log(2024) log(n) = -2025(3.30621058) log(n) = -6695.076279 n = 10^(-6695.076279) n = 10^(-6695)*10^(-0.076279) n = 10^(-6695)*0.8389208728 Divide the 10^(-6695) by 10 and multiply the 0.8389208728 by 10 n = 10^(-6696)*8.389208728 approximately 8.3892078728... × 10^-6696 in scientific notation. Edwin