Solve for m :

(4/7)^3m / (4/7) ^-6= (4/7)^-9

Asked by Cl_narayan | 17th Jun, 2019, 05:43: PM

Expert Answer:

begin mathsize 16px style open parentheses 4 over 7 close parentheses to the power of 3 straight m end exponent space divided by space open parentheses 4 over 7 close parentheses to the power of negative 6 end exponent space equals space open parentheses 4 over 7 close parentheses to the power of negative 9 end exponent
rightwards double arrow open parentheses 4 over 7 close parentheses to the power of 3 straight m space minus space left parenthesis negative 6 right parenthesis space space end exponent equals space open parentheses 4 over 7 close parentheses to the power of negative 9 end exponent space space space space space space...... space space since space space straight a to the power of straight m space divided by space space 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
rightwards double arrow open parentheses 4 over 7 close parentheses to the power of 3 straight m space plus space 6 space space end exponent equals space open parentheses 4 over 7 close parentheses to the power of negative 9 end exponent
rightwards double arrow 3 straight m space space equals space minus 15 space space space space space space space space space space space space space space space space space space space space space space space.... space since space space straight a to the power of straight x space equals space space space straight a to the power of straight y rightwards double arrow space straight x space equals space straight y
rightwards double arrow text m end text space equals space minus 5 end style

Answered by Yasmeen Khan | 17th Jun, 2019, 05:56: PM