Question

2. Simplify
16 x ^n+1 - 4x2^n
16x 24+2^n+2 - 2x 2^n+2​

Answer 1

Step-by-step explanation:

1 )Given.

= (16x2^n+1)-4x2^n / (16x2^n+2)-2x2^n+2

Take 2^n out since it is common on both sides in numerator i.e

= 2^n(16*2-4)/2^n + 2(16-2)

= 28/56

= 1/2

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2)(16*2n+1  -  4*2n) / (16*2n+2  -  2*2n+2)

= (24*2n+1  -  22*2n) / (24*2n+2 -  2*2n+2)        ( by using property  am * an= am+n)

= (24+n+1 - 2n+2) / (24+n+2 - 21+n+2)

= (2n+5-2n+2) / (2n+6-2n+3)

= (2n+2+3-2n+2) / (2n+3+3-2n+3)

= (2n+2)(2n+3-1) / (2n+3)(2n+3-1)

= 2n+2 / 2n+3

= 2n+2-(n+3)                     (by using property  am/an=am-n)

= 2n+2-n-3

= 22-3

= 2-1

=1/2

Hope it helps : )