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

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

Evaluate

$$x+\sqrt{x}$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

Use the distributive property to multiply x^{-\frac{1}{2}} by x+x^{\frac{3}{2}}.

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

To multiply powers of the same base, add their exponents. Add -\frac{1}{2} and 1 to get \frac{1}{2}.

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

To multiply powers of the same base, add their exponents. Add -\frac{1}{2} and \frac{3}{2} to get 1.

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

Calculate x to the power of 1 and get x.

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

Factor

$$\sqrt{x}\left(\sqrt{x}+1\right)$$