Question

Please answer me fast it is so urgent .

Answer 1

Given, expression

• $\sf{\dfrac{16*2^{n+1}-4*2^n}{16*2^{n+2}-2*2^{n+2}}}$

Solution:-

• To simplify this expression we have to split the terms or separate the terms individually.

$\rm{\implies \dfrac{16*2^n*2^1\:-4*2^n}{16*2^n*2^2\:-2*2^n*2^2}}$

• $\sf{by\: taking\: common\:2^n\:here}$

$\rm{\implies \dfrac{2^n(16*2^1\:-4)}{2^n(16*2^2\:-2*2^2)}}$

$\rm{\implies \dfrac{2^n(16*2-4)}{2^n(16*4-2*4)}}$

$\rm{\implies \dfrac{32-4}{64-8}}$

$\rm{\implies \cancel{\dfrac{28}{56}}}$

$\rm\red{\implies \dfrac{1}{2}}$

$\rm\purple{Some\:related\: Formula\:to\:\: this\:Question:-}$

$\rm{\implies a^m*a^n=a^{m+n}}$

$\rm{\implies a^m\div a^n=a^{m-n}}$

$\rm{\implies (a^m)^n=(a)^{mn}}$

$\rm{\implies a^0=1}$

$\rm{\implies (\frac{a}{b})^n=\frac{a^n}{b^n}}$

Answer 2

$\huge\purple{\rm{\underline{\underline{Answer :-}}}}$

(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