​ If 2^-m × 1/2^m = 1/4 , then 1/14 ((4^m)^1/2+(1/5^m)^-1) is equal to ​

Question

If 2^-m× \(\frac{1}{{2}^m}\) = \(\frac{1}4\) , then \(\frac{1}{14}\)\(\{(4^m)^{\frac{1}{2}}+(\frac{1}{5^m})^{-1}\}\) is equal to

A. \(\frac{1}2\)

B. 2

C. 4

D.\(-\frac{1}4\)

Answer 1

2^-m × 1 / 2^m = 1/4 

= 1/2^m × 1/2^m = 1/4 

= 1/4^m = 1/4 

= m = 1

1/14 {(4^m)^1/2 + (1/5^m) ^-1}

= 1/14 {2 + 5}

= 1/14 × 7

=  \(\frac{1}2\)