Solve (x^2-16)({x}^frac{1{2}})

$$( { x }^{ 2 } -16)( { x }^{ \frac{ 1 }{ 2 } } )$$

Evaluate

$$\sqrt{x}\left(x^{2}-16\right)$$

Solution Steps

Use the distributive property to multiply x^{2}-16 by x^{\frac{1}{2}}.

$$x^{2}x^{\frac{1}{2}}-16x^{\frac{1}{2}}$$

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

$$x^{\frac{5}{2}}-16x^{\frac{1}{2}}$$

Factor

$$\sqrt{x}\left(x-4\right)\left(x+4\right)$$