How do you simplify $\frac{4 x^{2}}{2 x^{\frac{1}{2}}}$ $(4x^2)/(2x^(1/2))$ ?

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Answer 1 · 2017-02-05T07:46:41

$2 x^{\frac{3}{2}}$ $2x^(3/2)$

Start with

$\frac{4 x^{2}}{2 x^{\frac{1}{2}}}$ $(4x^2)/(2x^(1/2)$

I'm going to first break this down so that we have constants in one fraction and $x$ $x$ terms in the other:

$(\frac{4}{2}) (\frac{x^{2}}{x^{\frac{1}{2}}})$ $(4/2)(x^2/x^(1/2))$

Let's do $\frac{4}{2}$ $4/2$ first - it's $\frac{4}{2} = 2$ $4/2=2$

Now let's do the $x$ $x$ terms. We can use $x^{a} \div x^{b} = x^{a - b}$ $x^a -: x^b=x^(a-b)$ to write our fraction as:

$x^{2} \div x^{\frac{1}{2}} = x^{2 - \frac{1}{2}} = x^{\frac{3}{2}}$ $x^2 -: x^(1/2)=x^(2-1/2)=x^(3/2)$

Putting it all together, we get:

$2 x^{\frac{3}{2}}$ $2x^(3/2)$

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