How do you solve $x^{\frac{3}{2}} - 10 x^{\frac{1}{2}} = 0$ $x^(3/2) - 10x^(1/2) = 0$ ?

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Answer 1 · 2015-10-20T15:16:00

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

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

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

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

$x^{\frac{1}{2}} [x^{\frac{2}{2}} - 10] = 0$ $x^(1/2)[x^(2/2)-10]=0$

$x^{\frac{1}{2}} [x - 10] = 0$ $x^(1/2)[x-10]=0$

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

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

How do you solve x32−10x12=0x^(3/2) - 10x^(1/2) = 0 ?