Question

55 points.
Please simplify it .
Don't answer of your don't know.
​

Answer 1

( i )
`\boxed{1}`

( ii )
`\boxed{2^(6n - 3m - 2)* 3^(3 - m)}`

.

Explanation:

( Part i )

`\left((1)/(x^(a - b)) \right)^(a + b)\left((1)/(x^(b + a)) \right)^(b - a)`

`= \left((1)/(x^((a - b)(a + b))) \right)\left((1)/(x^((b + a)(b - a))) \right)`

`= \left((1)/(x^(a^2 - b^2)) \right)\left((1)/(x^(b^2-a^2)) \right)`

`= (1)/(x^(a^2 - b^2 + (b^2 - a^2)))`

`= (1)/(x^0)`

`= (1)/(1)`

`= \boxed{1}`

.

( Part ii )

`(2^(m + n)* 3^(2m + 3) * 4^(2n -1))/(6^(2m + n)* 12^(m - n))`

`=(2^(m + n)* 3^(2m + 3) * 2^(2(2n -1)))/((2*3)^(2m + n)* (3* 2^2)^(m - n))`

`=(2^(m + n)* 3^(2m + 3) * 2^(4n -2))/(2^(2m + n)*3^(2m + n)* 3^(m - n)* 2^(2(m - n)))`

`=(2^(m + n + 4n - 2)* 3^(2m + 3))/(2^(2m + n + 2m - 2n)*3^(2m + n + m - n))`

`=(2^(m + 5n - 2)* 3^(2m + 3))/(2^(4m - n)*3^(3m))`

`= 2^(m + 5n - 2 - (4m - n))*3^(2m + 3 - 3m)`

`= \boxed{2^(6n - 3m - 2)* 3^(3 - m)}`

.

Happy to help :)

Answer 2

Explanation:

i) answer =1

ii) 2 -3m + 6n -2 x 3 3-m