I would like to know why the result of this exercise is "10x"

Question

The resolution of this exercise $(2\sqrt{x})*(5\sqrt[3]{x})$ is 10x. But I can't understand the steps to reach that result, since when I try to solve it, I get to:

$(2\sqrt{x})\cdot(5\sqrt[3]{x})$
$5 \cdot 2$
$(\sqrt{x}) = x ^ \frac{1}{2}$ and $(\sqrt[3]{x}) = x ^ \frac{1}{3}$
$x ^ \frac{1}{2} \cdot x ^ \frac{1}{3} = x ^ \frac{5}{6}$
$ 10x ^ \frac{5}{6} $

I would like to know how it is resolved

I copied it here and it tells me that the result is 10x https://es.symbolab.com/solver/step-by-step/%5Cleft(2%5Csqrt%7Bx%7D%5Cright)%5Ccdot%5Cleft(5%5Csqrt%5B3%5D%7Bx%7D%5Cright) — Lucas Damian, Nov 18 '19 at 14:45
@LucasDamian It seems Symbolab is not parsing the cube root properly. https://es.symbolab.com/solver/step-by-step/%5Cleft(2%5Csqrt%7Bx%7D%5Cright)%5Ccdot%5Cleft(5x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Cright) — 79037662, Nov 18 '19 at 15:00

score 1 · Accepted Answer · answered Nov 18 '19 at 14:59

1

It is $$10x^{1/2}\times x^{1/3}=10x^{1/2+1/3}=10x^{\frac{3+2}{6}}=10x^{5/6}$$

answered Nov 18 '19 at 14:59

Dr. Sonnhard Graubner

95,283

I would like to know why the result of this exercise is "10x"

1 Answers1