Question

Simplify (2^2n-3.2^2n-2)(3^n-2.3^n-2)/3^n-4(4^n+3-2^2n)​

Answer 1

Step-by-step explanation:

Now, $\displaystyle\frac{(2^{2n-3}.2^{2n-2})(3^{n-2}.3^{n-2})}{3^{n-4}(4^{n+3}-2^{2n})}$

$\displaystyle=\frac{2^{2n-3+2n-2}.3^{n-2+n-2})}{3^{n-4}((2^{2})^{n+3}-2^{2n})}$

$\displaystyle=\frac{2^{4n-5}.3^{2n-4}}{3^{n-4}(2^{2n+6}-2^{2n})}$

$\displaystyle=\frac{2^{4n-5}.3^{2n-4}}{3^{n-4}.2^{2n}(2^{6}-1)}$

$\displaystyle=\frac{2^{4n-5}.3^{2n-4}.3^{-(n-4)}.2^{-(2n)}}{2^{6}-1}$

$\displaystyle=\frac{2^{4n-5}.2^{-2n}.3^{2n-4}.3^{-n+4}}{2^{6}-1}$

$\displaystyle=\frac{2^{4n-5-2n}.3^{2n-4-n+4}}{2^{6}-1}$

$\displaystyle=\frac{2^{2n-5}.3^{n}}{2^{6}-1}$

This is the required simplified form.

Answer:

The required simplified form is

$\quad\quad\quad \displaystyle \frac{2^{2n-5}.3^{n}}{2^{6}-1}$.

Note:

However if needed, the last form can be simplified further by evaluating $\displaystyle 2^{5}=32$ and $\displaystyle 2^{6}=64$.

Answer 2

Step-by-step explanation:

see the attached image above....

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