S i m p l i f y space colon space fraction numerator 16 x 2 to the power of n plus 1 end exponent minus 4 x 2 to the power of n over denominator 16 x 2 to the power of n plus 2 end exponent minus 2 x 2 to the power of n plus 2 end exponent end fraction

Asked by kishor.kp14 | 22nd Jun, 2019, 10:19: AM

Expert Answer:

begin mathsize 16px style fraction numerator 16 cross times 2 to the power of straight n plus 1 end exponent space minus space 4 cross times 2 to the power of straight n over denominator 16 space cross times 2 to the power of straight n plus 2 end exponent space minus space 2 cross times 2 to the power of straight n space plus space 2 end exponent end fraction
equals space fraction numerator begin display style 16 cross times space 2 space cross times 2 to the power of straight n space minus space 4 cross times 2 to the power of straight n end style over denominator begin display style 16 space cross times 2 squared cross times 2 to the power of straight n space minus space 2 cross times space 2 squared cross times 2 to the power of straight n end style end fraction space space space space space space space... space since space straight a to the power of straight m space 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 fraction numerator 4 space cross times 2 to the power of straight n open parentheses 8 space minus space 1 close parentheses over denominator 4 space cross times 2 to the power of straight n open parentheses 16 space minus 2 close parentheses end fraction
equals 7 over 14
equals 1 half end style

Answered by Yasmeen Khan | 23rd Jun, 2019, 11:11: AM