Question

simplify 16 into 2 to the power n + 1 - 4 to the power 2n upon 16 into 2 to the power n + 2 - 2 into 2 to the power n + 2​

Answer 1

I think u should check it question once...

Answer 2

The value of given expression is 1/2.

Step-by-step explanation:

Consider the given expression is

$\dfrac{16\times 2^{n+1}-4\times 2^{n}}{16\times 2^{n+2}-2\times 2^{n+2}}$

It can be rewritten as

$\dfrac{16\times 2^{n+1}-2\times (2\cdot 2^{n})}{16\times 2^{n+2}-2\times 2^{n+2}}$

$\dfrac{16\times 2^{n+1}-2\times 2^{n+1}}{16\times 2^{n+2}-2\times 2^{n+2}}$                  $[\because a^m\cdot a^n=a^{m+n}]$

Taking out common factors.

$\dfrac{(16-2)\times 2^{n+1}}{(16-2)\times 2^{n+2}}$

$\dfrac{14\times 2^{n+1}}{14\times 2^{n+2}}$

Cancel out common factors.

$\dfrac{2^{n+1}}{2^{n+2}}$

$2^{n+1-n-2}$                 $[\because \dfrac{a^m}{a^n}=a^{m-n}]$

$2^{-1}$

$\dfrac{1}{2}$

Therefore, the value of given expression is 1/2.

#Learn more

(49)^3/2-(49)^5/2/49

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