Stupid indices question (1 Viewer)

[Mr. Osama]

a. (12^x + 1)/ (6^2x + 3^x)

b. (2^2n+2) - (2^2n-1)

i am stuck on these two....plz help.

 

[acmilan]

(a)
(12^x + 1)/(6^2x + 3^x)
= ([4.3]^x + 1)/([3.2]^2x + 3^x)
= (4^x3^x + 1)/(3^2x2^2x + 3^x)
= (2^2x3^x + 1)/(3^2x2^2x + 3^x)
= (2^2x3^x + 1)/(3^x(3^x2^2x + 1)
= 1/3^x

(b)
2²ⁿ⁺² - 2^2n-1
= 2²ⁿ2² - 2²ⁿ2^-1
= 2²ⁿ(2² - 2^-1)
= 2²ⁿ(4 - (1/2))
= 2²ⁿ(7/2)
= 7.2^2n-1

 

[Mr. Osama]

thankyou acmilan..that was great help.