Equality

[WMStudent22]

Can someone explain to me why the right one is the 'way to go'? I do not understand this step.

Many thanks in advance.

 

[Deleted member 4993]

View attachment 22106

Can someone explain to me why the right one is the 'way to go'? I do not understand this step.

Many thanks in advance.

At the numerator (of LeftHandSide), it should have been:

\(\displaystyle \frac{(x^{\frac{1}{3}}* y^{\frac{2}{3}})^9*x^2}{y}\)

 

[Steven G]

... because you did not write cube root of x.

[MATH]\sqrt[3]{xy^2} = \sqrt[3]{x} \sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]
How can I get the two cube roots signs to be the same size??

 

[Deleted member 4993]

How can I get the two cube roots signs to be the same size??

Why..... is it making you go cross-eyed??

Anyway, the short answer is - I do not know "why"? Tried different "things" - but did not work>

 

[jonah2.0]

Beer soaked ideas follow.

[MATH]\sqrt[3]{xy^2} = \sqrt[3]{x} \sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]
How can I get the two cube roots signs to be the same size??

With capital X and Y, still not the same size
[MATH]\sqrt[3]{XY^2} = \sqrt[3]{X}\sqrt[3]{Y^2} = X^{1/3}Y^{2/3}[/MATH]But with [MATH]X^1[/MATH][MATH]\sqrt[3]{XY^2} = \sqrt[3]{X^1}\sqrt[3]{Y^2} = X^{1/3}Y^{2/3}[/MATH]No cigar with
[MATH]\sqrt[3]{xy^2} = \sqrt[3]{x^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]Enclosing x in parentheses, it looks as if they are almost the same size (in the 2nd case).
Maybe it's just me beer goggles.
[MATH]\sqrt[3]{xy^2} = \sqrt[3]{\big(x\big)^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH][MATH]\sqrt[3]{xy^2} = \sqrt[3]{(x)^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH][MATH]\sqrt[3]{xy^2} = \sqrt[3]{\big(x\big)}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]

 

[Deleted member 4993]

Beer soaked ideas follow.

With capital X and Y, still not the same size
[MATH]\sqrt[3]{XY^2} = \sqrt[3]{X}\sqrt[3]{Y^2} = X^{1/3}Y^{2/3}[/MATH]But with [MATH]X^1[/MATH][MATH]\sqrt[3]{XY^2} = \sqrt[3]{X^1}\sqrt[3]{Y^2} = X^{1/3}Y^{2/3}[/MATH]No cigar with
[MATH]\sqrt[3]{xy^2} = \sqrt[3]{x^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]Enclosing x in parentheses, it looks as if they are almost the same size (in the 2nd case).
Maybe it's just me beer goggles.
[MATH]\sqrt[3]{xy^2} = \sqrt[3]{\big(x\big)^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH][MATH]\sqrt[3]{xy^2} = \sqrt[3]{(x)^1}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH][MATH]\sqrt[3]{xy^2} = \sqrt[3]{\big(x\big)}\sqrt[3]{y^2} = x^{1/3}y^{2/3}[/MATH]

There Jomo - you don't have to go cross-eyed anymore .....