Question

If 2^m+n/2^n-m =16 and a= 2^1/10, then
a^2m+n-p/(a^m-2n+2p)^ -1 is equal to?

(RD SHARMA, CLASS IX, CHAPTER 2, MCQs, QUESTION-37)

(a) 2
(b) 1/4
(c) 9
(d) 1/8​

Answer 1

first of all

simply every term in its exponential form

$\frac{{2}^{m + n}}{ {2}^{n - m } } = {2}^{4}$

now

bases are common

${2}^{(m + n -( n - m))} = {2}^{4}$

${2}^{2m} = {2}^{4}$

cancel the bases on both the sides

$2m = 4 \\ \\ m = \frac{4}{2} = 2$

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