Question

a)\(\dfrac{2\times6^9-2^5\times18^4}{2^2\times6^8}\)   

Answer 1

`(2 . 6^9 - 2^5 . 18^4)/(2^2 . 6^8)`

`= (2 . (2 . 3)^9 - 2^5 . (2 . 3^2)^4)/(2^2 . (2 . 3)^8)`

`= (2 . 2^9 .3^9 - 2^5 . 2^4 . 3^8)/(2^2 . 2^8 . 3^8)`

`= (2^10 . 3^9 - 2^9 . 3^8)/(2^10 . 3^8)`

`= (2^9 . 3^8 . (2 . 3 - 1))/(2^9 . 3^8 . 2)`

`= (6-1)/2`

`= 5/2`

Answer 2

\(\dfrac{2\cdot6^9-2^5\cdot18^4}{2^2\cdot6^8}=\dfrac{2\cdot2^9\cdot3^9-2^5\cdot2^4\cdot3^8}{2^2\cdot2^8\cdot3^8}\)

\(=\dfrac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{10}\cdot3^8}\)

\(=\dfrac{2^9\cdot3^8\left(2\cdot3-1\right)}{2^{10}\cdot3^8}=\dfrac{1}{2}\cdot5=\dfrac{5}{2}\)