Example 1 Simplify the following a 64 frac 5 6 ... - SS1 Mathematics Number Forms (Indices And Logarithm) Question

Solution (a) \(64^{\frac{5}{6}} = \ \sqrt[6]{64^{5}} = \ \sqrt[6]{{(2^{6})}^{5}} = \ \sqrt[6]{2^{6 \times 5}} = \ 2^{\frac{6 \times 5}{6}} = \ 2^{5} = 32\)

(b) \(40^{5} \div 40^{3} = \ 40^{5 - 3} = \ 40^{2} = 1600\)

(c) \({(5^{\frac{1}{- 2}})}^{4} = \ 5^{\frac{1}{- 2} \times \frac{4}{1}} = \ 5^{\frac{4}{- 2}} = \ 5^{- 2} = \ \frac{1}{5^{2}} = \ \frac{1}{25}\)