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If \(x^{x\sqrt{x}} = (x\sqrt{x})^x. then\, x\,is\,equal\,to\)

(a) \(\frac32\) 

(b) \(\frac29\) 

(c) \(\frac94\) 

(d) \(\frac49\)

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(c) \(\frac94\)
\(x^{x\sqrt{x}} = (x\sqrt{x})^x\)

⇒ \(x^{x\sqrt{x}} = (x^{\frac32})^x\) ⇒ \(x^{x\sqrt{x}} =x^{\frac{3}{2}x}\)

⇒ \(x\sqrt{x} = \frac32x ⇒\sqrt{x} =\frac32⇒x=\frac94.\)

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