What is expand x^{1/2 (x^{-3/2}+x^{-1/2})} ?

The solution to expand x^{1/2 (x^{-3/2}+x^{-1/2})} is x^{1/(2x^{3/2)}+1/(2x^{1/2)}}

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expand x^{1/2 (x^{-3/2}+x^{-1/2})}

expand

x^{\frac{1}{2} (x^{- \frac{3}{2}} + x^{- \frac{1}{2}})}

x^{\frac{1}{2 x ^{\frac{3}{2}}} + \frac{1}{2 x ^{\frac{1}{2}}}}

Solution steps

x^{\frac{1}{2} (x^{- \frac{3}{2}} + x^{- \frac{1}{2}})}

Simplify

x^{- \frac{3}{2}} + x^{- \frac{1}{2}} : \frac{1}{x ^{\frac{3}{2}}} + \frac{1}{x ^{\frac{1}{2}}}

= x^{\frac{1}{2} (\frac{1}{x ^{\frac{3}{2}}} + \frac{1}{x ^{\frac{1}{2}}})}

Expand

\frac{1}{2} (\frac{1}{x ^{\frac{3}{2}}} + \frac{1}{x ^{\frac{1}{2}}}) : \frac{1}{2 x ^{\frac{3}{2}}} + \frac{1}{2 x ^{\frac{1}{2}}}

= x^{\frac{1}{2 x ^{\frac{3}{2}}} + \frac{1}{2 x ^{\frac{1}{2}}}}

\frac{( x - 1 ) ( x ^{2} + 1 )}{x ^{2} - 3}

9 (2 w - e)

lo g_{10} (\frac{x y ^{2}}{2 m})

\frac{d}{d y} ((x y^{2} - 1) e^{x}) - y^{2} e^{x}

\frac{\partial}{\partial x} (x^{2}) + 2 y + λ (x - 2 y)

What is expand x^{1/2 (x^{-3/2}+x^{-1/2})} ?
The solution to expand x^{1/2 (x^{-3/2}+x^{-1/2})} is x^{1/(2x^{3/2)}+1/(2x^{1/2)}}