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Number Systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber Systems2 Marks
Question
Simplify: $(256)^{-\Big(4^{-\frac{3}{2}}\Big)}$
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Answer

$(256)^{-\Big(4^{-\frac{3}{2}}\Big)}=(256)^{-(4)^{-\frac{3}{2}}}=(256)^{-(2^2)^{-\frac{3}{2}}}$ $=(256)^{-\Big(2^{2\times-\frac{3}{2}}\Big)}=(256)^{-(2^{-3})}$ $\Big[\because\ \text{(b)}^{(\text{a}^\text{m})^\text{n}}=\text{b}^{\text{a}^\text{mn}}\Big]$ $=(2^8)^{-\Big(\frac{1}{2^3}\Big)}=(2^8)^{-\frac{1}{8}}$ $=2^{8\times-\frac{1}{8}}=2^{-1}=\frac{1}{2}$

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