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Q2. a. Simplify the following as fully as possible:  (3a² bc⁴)²/(a³ b⁶ c⁹)^1/3  (4)

b. Solve the following equation for x: 4^2x-1 = 8^{2x + 1}  (4)

c. The value of a vessel at any age can be determined from the formula:

R_V= C[1 - r/100]ⁿ  where n = age of the vessel in years

r/100 = The annual rate of depreciation as a percentage

C = value of the vessel when new in £M

R_V  = Residual value of the vessel after n years in £M

Use the formula to determine how long it will take a vessel, which cost £23 M to build and depreciates in value by 16 % each year, to fall to its scrap value or £O.92 M. (8)