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Q3. (a) The value, V, in thousands of pounds, of a propulsion unit after t years is given by:

V = 275e^{- 0.085t}

Calculate EACH of the following for the propulsion unit:

(i) the initial value; (2)

(ii) the number of complete years before its value is less than £100k. (6)

(b) Use laws of indices to simplify EACH of the following:

(i) ((75 a^3/8)/(25 a^1/4)) (4)

(ii) (x²/y⁴ )^-1/2 × (y³/x^-6)^1/3