The solution to the equation (x)^{xsqrt{x}} = | vedclass

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(A) Given the equation: $(x)^{x\sqrt{x}} = (x\sqrt{x})^x$We can rewrite the right side as: $(x \cdot x^{1/2})^x = (x^{3/2})^x = x^{3x/2}$So,the equati

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$9/4$

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(A) Given the equation: $(x)^{x\sqrt{x}} = (x\sqrt{x})^x$We can rewrite the right side as: $(x \cdot x^{1/2})^x = (x^{3/2})^x = x^{3x/2}$So,the equation becomes: $x^{x\sqrt{x}} = x^{3x/2}$This implies $x^{x^{3/2}} = x^{3x/2}$Equating the exponents: $x^{3/2} = \frac{3x}{2}$Dividing by $x$ (assuming $x 
eq 0$): $x^{1/2} = \frac{3}{2}$Squaring both sides: $x = (\frac{3}{2})^2 = \frac{9}{4}$Thus,the solution is $x = \frac{9}{4}$.

The solution to the equation $(x)^{x\sqrt{x}} = (x\sqrt{x})^x$ is:

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