Show that (a ^ (x - y)) ^ (x + y) * (a(y - 2)) ^ (y + 2) * (a ^ (2 - x)) ^ (z + x) = 1

Asked by anuachu8792 | 12th Jul, 2021, 01:13: PM

Expert Answer:

Consider,
open parentheses straight a to the power of straight x minus straight y end exponent close parentheses to the power of open parentheses straight x plus straight y close parentheses end exponent asterisk times open parentheses straight a to the power of straight y minus straight z end exponent close parentheses to the power of open parentheses straight y plus straight z close parentheses end exponent asterisk times open parentheses straight a to the power of straight z minus straight x end exponent close parentheses to the power of open parentheses straight z plus straight x close parentheses end exponent
equals straight a to the power of open parentheses straight x squared minus straight y squared close parentheses end exponent asterisk times straight a to the power of open parentheses straight y squared minus straight z squared close parentheses end exponent asterisk times straight a to the power of open parentheses straight z squared minus straight x squared close parentheses end exponent
equals straight a to the power of straight x squared minus straight y squared plus straight y squared minus straight z squared plus straight z squared minus straight x squared end exponent
equals straight a to the power of 0
equals 1
Hence comma space open parentheses straight a to the power of straight x minus straight y end exponent close parentheses to the power of open parentheses straight x plus straight y close parentheses end exponent asterisk times open parentheses straight a to the power of straight y minus straight z end exponent close parentheses to the power of open parentheses straight y plus straight z close parentheses end exponent asterisk times open parentheses straight a to the power of straight z minus straight x end exponent close parentheses to the power of open parentheses straight z plus straight x close parentheses end exponent equals 1

Answered by Renu Varma | 15th Jul, 2021, 08:10: PM