Question

PROVE YOUR TALENT BY SOLVING THIS BRILLIANT QUESTION..........

Answer 1

2 to the power -27/25 – 1....
now by solving this ur ans will be ready
I give u almost 80% hint of that question

Answer 2

Well, from equation first,
Using
$\frac{a {}^{m} }{a {}^{n} } = a {}^{m - n}$
So from this:
$\frac{2 {}^{m + n} }{2 {}^{n - m} } \: = 2 {}^{2m}$
and
${2}^{2m} \: = 2 {}^{4}$
From this m =2 (Equation x)

Similarly from equation second

$\frac{ {3}^{p} }{ {3}^{n} } = 81$
p-n=4 (equation y)

Now from third equation

$\frac{ {a}^{2m + n - p} }{( {a}^{m - 2n + 2p}) {}^{ - 1} }$

So,
${a}^{2m + n - p + m - 2n + 2p}$
${a}^{3m + p - n}$
From eq x and y
${a}^{6 + 4} = {a}^{10}$

Now, finallly putting value of a

We get

$(2 {}^{1 \div 10 ){}^{10} } = 2$
Ans. 2