What is 1/3 x^{3/2}-x^{1/2} ?

The solution to 1/3 x^{3/2}-x^{1/2} is (x^{3/2})/3-x^{1/2}

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simplify 1/3 x^{3/2}-x^{1/2}

simplify

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

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

Solution steps

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

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{1}{3} x^{\frac{3}{2}} = \frac{1 \cdot x ^{\frac{3}{2}}}{3}

= \frac{1 \cdot x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}}

Apply rule:

1 \cdot a = a

1 \cdot x^{\frac{3}{2}} = x^{\frac{3}{2}}

= \frac{x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}}

What is 1/3 x^{3/2}-x^{1/2} ?
The solution to 1/3 x^{3/2}-x^{1/2} is (x^{3/2})/3-x^{1/2}