Question 1194326
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I'm on radical Quotient property. I'm trying to understand where my tutorial is getting x over y = xy^-1

kind of like

cubic root of x^2 * y 	over
cubic root of 8*x*y^2	

which is rewritten as the cubic root of the entire fraction by applying  
Quotient property

similar to

Cubic root of
x^2*y over
8*x*y^2

1 of the x's and 1 of the y's cancel each other out because exponent's Quotient property

so now we have

Cubic root of
x over
8y

now we apply Product Property and get

cubic root of
1 over 8 * x over y

I understand 1*x=x and 8*y=8y but here is where my tutorial loses me. They have

cubic root of 1 over cubic root of 8 * cubic root of xy^-1

the explanation is "Quotient property and x over y = xy^-1"
this makes no sense to me. Is this just a fact?

they then rewrite

cubic root of
1 over 8 * x over y

again saying "Quotient property and x over y = xy^-1"

finally 

1 over 2 cubic root xy^-1         "Our solution"</pre>
<pre>This is EXACTLY how itw's done:
{{{highlight_green(matrix(1,15, root(3, x^2y)/root (3, 8xy^2), "=", root(3, x^2y/(8xy^2)), "=", root(3, x*cross(x^2)cross(y)/(8cross(x)y*cross(y^2))), "=", root(3, x/(8y)), "=", root(3, (1/8)(x/y)), "=", root(3, (1^3/2^3)(x/y)), "=", (1/2)root(3, x/y), ",  or", highlight((1/2)root(3, xy^(- 1)))))}}}