# How do you solve x^(3/2) - 10x^(1/2) = 0 ?

Oct 20, 2015

$x = 0$ OR $x = 10$

#### Explanation:

We can factor out fractional exponents. Since the base $\left(x\right)$ is the same.

Look at the fractional exponent that is the least and proceed as follows:

Remember your properties for exponents ${x}^{m} {x}^{n} = {x}^{m + n}$

${x}^{\frac{1}{2}} \left[{x}^{\frac{2}{2}} - 10\right] = 0$

${x}^{\frac{1}{2}} \left[x - 10\right] = 0$

${x}^{\frac{1}{2}} = 0$ OR $x - 10 = 0$

So $x = 0$ OR $x = 10$