Theory question 103
Indices(a) Simplify: 6253/8 × 51/2 ÷ 25
(b) Solve the following equations, correct to one decimal place. (i) tan (θ + 25°) = 5.145 (ii) 5 cos θ − 1 = 0, where 0 ≤ θ ≤ 90°
Show the model answer
Model answer
(a) 6253/8 = (54)3/8 = 53/2. 53/2 × 51/2 ÷ 52 = 50 = 1.
(b)(i) θ + 25° = tan−15.145 = 79.0°, so θ = 54.0°.
(ii) cos θ = 0.2, so θ = 78.5°.
Explanation
Write 625 and 25 as powers of 5.