Theory question 102
Coordinate Geometry(a) Evaluate: 2 ÷ (64/125)−2/3
(b) The lines y = 3x + 5 and y = −4x − 1 intersect at a point k. Find the coordinates of k.
Show the model answer
Model answer
(a) Dividing by a negative power is multiplying by the positive power: 2 × (64/125)2/3 = 2 × (4/5)2 = 2 × 16/25 = 32/25 = 1 7/25.
(b) 3x + 5 = −4x − 1, so 7x = −6 and x = −6/7.
y = 3(−6/7) + 5 = 17/7 = 2 3/7. K = (−6/7, 2 3/7).
Explanation
(64/125)^(1/3) = 4/5; then square it.