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Q. Which one is NOT equal to \( \left(\frac{100}{9}\right)^{-\frac{3}{2}} \) ?
(a) \( \left(\frac{9}{100}\right)^{\frac{3}{2}} \)
(b) \( \frac{1}{\left(\frac{100}{9}\right)^{\frac{3}{2}}} \)
(c) \( \frac{3}{10} \times \frac{3}{10} \times \frac{3}{10} \)
(d) \( \sqrt{\frac{100}{9} \times \frac{100}{9} \times \frac{100}{9}} \)
✏️ Solution
\( \left(\frac{100}{9}\right)^{-\frac{3}{2}} = \left(\frac{9}{100}\right)^{\frac{3}{2}} \)
\( = \left(\frac{3}{10}\right)^3 \)
\( = \frac{27}{1000} \)
(a) \( \left(\frac{9}{100}\right)^{3/2} = \frac{27}{1000} \)
(b) \( \frac{1}{\left(\frac{100}{9}\right)^{3/2}} = \frac{27}{1000} \)
(c) \( \frac{3}{10}\times\frac{3}{10}\times\frac{3}{10} = \frac{27}{1000} \)
(d) \( \sqrt{\left(\frac{100}{9}\right)^3} = \left(\frac{100}{9}\right)^{3/2} \neq \frac{27}{1000} \)
Correct Option: (d)
\( \boxed{(d)} \)