(a) \(625^{\frac{3}{8}} \times 5^{\frac{1}{2}} \div 25\) = \((5^{4})^{\frac{3}{8}} \times 5^{\frac{1}{2}} \div 5^{2}\) = \(5^{\frac{3}{2}} \times 5^{\frac{1}{2}} \div 5^{2}\) = \(5^{\frac{3}{2} + \frac{1}{2} - 2}\) = \(5^{0} = 1\) (b)(i) \(\tan (\theta + 25)^\circ = 5.145\) \(\theta + 25 = \tan^{-1} (5.145)\) \(\implies \theta + 25 = 79^\circ\) \(\theta = 79^\circ - 25^\circ = 54^\circ\) (ii) \(5 \cos \theta - 1 = 0\) \(\implies 5 \cos \theta = 1\) \(\cos \theta = \frac{1}{5} = 0.2\) \(\theta = \cos^{-1} (0.2) = 78.463^\circ\) \(\approxeq 78.5^\circ\) (to one d.p)