Question

Simplify : (1/3)-2+(1/4)-2+(1/5)-2+(1/5)-2-(1/6)-2​

Answer 1

Answer:

Step-by-step explanation:

Exponent law:

(a / b)^-m = (b / a) ^m

Given:

(1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2

Step 1:

Apply

(a / b)^-m = (b / a) ^m in given expression

= (1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = (4 / 1)^2 + (2 /1)^2 + (3 / 1)^2

= (1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = 4^2 + 2^2 + 3^2

Step 2:

Expand equation (1)

= (1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = 4 x 4 + 2 x 2 + 3 x 3

= (1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = 16 + 4 + 9

= (1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = 29

Final answer

(1 / 4)^-2 + (1 / 2)^-2 + (1 / 3)^-2 = 29