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Number Systems — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumber Systems2 Marks
Question
Simplify: $64^{-\frac{1}{3}}64^{\frac{1}{3}}-64^{\frac{2}{3}}$
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Answer

$64^{-\frac{1}{3}}\Big[64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big]=(4^3)^{-\frac{1}{3}}\Big[(4^3)^{\frac{1}{3}}-(4^3)^{\frac{2}{3}}\Big]$ $4^{3\times-\frac{1}{3}}\Big(4^{3\times\frac{1}{3}}-4^{3\times\frac{1}{3}}\Big)=4^{-1}(4-4^2)$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$ $=\frac{1}{4}(4-16)=-\frac{12}{4}=-3$

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