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

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

Evaluate

$$\sqrt{x}\left(x-1\right)^{2}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{2} to get \frac{5}{2}.

$$x^{\frac{5}{2}}-2xx^{\frac{1}{2}}+x^{\frac{1}{2}}$$

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

$$x^{\frac{5}{2}}-2x^{\frac{3}{2}}+x^{\frac{1}{2}}$$

Factor

$$\sqrt{x}\left(x-1\right)^{2}$$