SOLUTION: 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 w

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Question 1194326: 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"
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Maybe I not follow your description well but x/y means the same as x*y^(-1). This is well defined notation and not a mystery.


"cubic root of
1 over 8 * x over y"
That is ambiguous.


"cubic root of x^2 * y over
cubic root of 8*x*y^2"
Again this is also ambiguous.


-----------

I saw and read your extra note. Most of the square root description is still too ambiguous. Show your starting expression clearly in correct notation to get the help you want.

As for , this is already clear. Nothing to not understand.

---

Is this what your expression is as given?



And if so, you wish to simplify this?
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

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"
This is EXACTLY how itw's done:

 

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