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Q. If \( \frac{x}{x^{1.5}} = 8x^{-1} \) and \( x > 0 \), find \( x \)
(a) \( \frac{\sqrt{2}}{4} \) (b) \( 2\sqrt{2} \) (c) 4 (d) 64
✏️ Solution
\( \frac{x}{x^{1.5}} = x^{1 – 1.5} \)
\( = x^{-0.5} \)
\( x^{-0.5} = 8x^{-1} \)
Multiply both sides by \( x \)
\( x^{0.5} = 8 \)
\( \sqrt{x} = 8 \)
\( x = 64 \)
Correct Option: (d) 64
\( \boxed{64} \)