solve the following
fraction numerator 16 cross times 2 to the power of n plus 1 end exponent minus 4 cross times 2 to the power of n over denominator 16 cross times 2 to the power of n plus 2 end exponent minus 2 cross times 2 to the power of n plus 2 end exponent end fraction

Asked by badesraajay | 16th Aug, 2015, 02:23: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n comma space fraction numerator 16 cross times 2 to the power of n plus 1 end exponent minus 4 cross times 2 to the power of n over denominator 16 cross times 2 to the power of n plus 2 end exponent minus 2 cross times 2 to the power of n plus 2 end exponent end fraction fraction numerator 16 cross times 2 to the power of n plus 1 end exponent minus 4 cross times 2 to the power of n over denominator 16 cross times 2 to the power of n plus 2 end exponent minus 2 cross times 2 to the power of n plus 2 end exponent end fraction equals fraction numerator 2 to the power of 4 cross times 2 to the power of n plus 1 end exponent minus 2 squared cross times 2 to the power of n over denominator 2 to the power of 4 cross times 2 to the power of n plus 2 end exponent minus 2 cross times 2 to the power of n plus 2 end exponent end fraction 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 fraction numerator 2 to the power of 4 cross times 2 to the power of n cross times 2 to the power of 1 minus 2 squared cross times 2 to the power of n over denominator 2 to the power of 4 cross times 2 to the power of n cross times 2 squared minus 2 cross times 2 to the power of n cross times 2 squared end fraction space space space space space space space space space open square brackets because a to the power of m plus n end exponent equals a to the power of m cross times a to the power of n close square brackets 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 fraction numerator 2 to the power of 4 cross times up diagonal strike 2 to the power of n end strike cross times 2 to the power of 1 minus 2 squared cross times up diagonal strike 2 to the power of n end strike over denominator 2 to the power of 4 cross times up diagonal strike 2 to the power of n end strike cross times 2 squared minus 2 cross times up diagonal strike 2 to the power of n end strike cross times 2 squared end fraction 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 fraction numerator 2 to the power of 4 cross times 2 to the power of 1 minus 2 squared over denominator 2 to the power of 4 cross times 2 squared minus 2 cross times 2 squared end fraction 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 fraction numerator 2 to the power of 4 minus 2 over denominator 2 to the power of 4 cross times 2 minus 2 cross times 2 end fraction 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 fraction numerator 16 minus 2 over denominator 16 cross times 2 minus 2 cross times 2 end fraction 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 fraction numerator 16 minus 2 over denominator 32 minus 4 end fraction 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 14 over 28 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 1 half

Answered by Vimala Ramamurthy | 17th Aug, 2015, 08:42: AM