{(1/3)^3}×(3/2)^2÷{(2/3)^–1}^3

Asked by rajubarman | 9th Sep, 2019, 08:17: PM

Expert Answer:

begin mathsize 16px style open parentheses 1 third close parentheses cubed cross times space open parentheses 3 over 2 close parentheses squared divided by open square brackets open parentheses 2 over 3 close parentheses to the power of negative 1 end exponent close square brackets cubed space
equals space 1 over 3 cubed cross times space 3 squared over 2 squared divided by open parentheses 3 over 2 close parentheses cubed space space space space space space space space space space space space space space.... space straight a to the power of negative straight m end exponent space equals space 1 over straight a to the power of straight m
equals 1 over 3 cubed space cross times space 3 squared over 2 squared cross times space 2 cubed over 3 cubed space space space space space space space space space space space space space space space space space space.... space space straight a to the power of straight m cross times space straight a to the power of straight n space equals space straight a to the power of straight m plus straight n end exponent
equals 3 squared over 3 to the power of 6 cross times 2 cubed over 2 squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space
equals space 2 over 3 to the power of 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... space space straight a to the power of straight m divided by space straight a to the power of straight n space equals space straight a to the power of straight m minus straight n end exponent
equals 2 over 81 end style

Answered by Yasmeen Khan | 11th Sep, 2019, 11:04: AM