Question

simply and give reasons 1+2power-1+3power-1+4°​

Answer 1

1 + 2^-1 + 3^-1 + 4^0
1 + 1/2 + 1/3 + 1
As any number with a negative power is equal to reciprocal of that number i.e. 2 to the power -1 is equal to 1/2
And any number having 0 as power is equal to 1 i.e. 4 to the power 0 is equal to 1
Back to the question
1 + 1/2 + 1/3 + 1
Multiply 1/2 with 3/3 and 1/3 with 2/2
1 + (1 X 3)/(2 X 3) + (1 X 2)/(3 X 2) + 1
1 + (3)/(6) + (2)/(6) + 1
Taking 6 as common, we get:
1 + (3 + 2)/6 + 1
1 + (5)/6 + 1
1 + 1 + 5/6
2 + 5/6
Multiply 2 with 6/6 and 5/6 with 1/1
As 2 also equal to 2/1
We get
2 X 6/6 + 5/6 X 1/1
12/6 + 5/6
Taking 6 as common
(12 + 5)/6
17/6