Question

A. Given that 2ᵐ* ( 1/8 )ⁿ=128 and 4ᵐ/ 2⁻⁴ⁿ= 1/16 , find the value of (m-n)

Answer 1

`{2}^(m) {( (1)/(8)) }^(n) = {2}^(m) ( {2}^( - 3n) ) = {2}^(m - 3n) = {2}^(7)`

`\frac{ {4}^(m) }{ {2}^( - 4n) } = {2}^(2m) {2}^(4n) =`

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

m - 3n = 7

m + 2n = -2

----------------

5n = -9

n = -1.8, m = 1.6

m - n = 1.6 - (-1.8) = 3.4