Simplify expression with laws of indices

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Discussion Overview

The discussion revolves around simplifying a mathematical expression involving laws of indices, specifically the expression (x-2y10)3 / (x-4yz4)-5. Participants explore various approaches to handle negative powers and the presence of the variable z in the denominator.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant expresses uncertainty about how to advise on the expression due to the presence of z only in the denominator.
  • Another participant proposes that z^(4*(-5)) can be simplified to z^(-20), suggesting that this leads to z^20 in the numerator.
  • A different participant emphasizes the importance of eliminating negative powers and outlines a strategy involving the transformation of the expression into a form that separates the variables.
  • This participant also provides a partial simplification of the expression, asking others to complete the process.
  • A later reply acknowledges the assistance received and notes that the basic rule discussed helped clarify the problem.

Areas of Agreement / Disagreement

There is no explicit consensus on the final simplification of the expression, as participants are contributing different approaches and some are still seeking clarification.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in simplifying the expression, and there are dependencies on the interpretation of negative powers and the handling of variables.

dmarley
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Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
 
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dmarley said:
(x-2y10)3 / (x-4yz4)-5
This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
z^(4*(-5)) = z^(-20)
Now move to numerator:
z^(-20) = z^20

So you'll end up with: y^35 * z^20 / x^26
 
dmarley said:
Helping my daughter with her math and hit this one and not sure how to advise. All help welcome(x-2y10)3 / (x-4yz4)-5

This one throws me off because I don't know how to deal with the z, as only on the right side of the divide
The basic rule is [math]a^{-1} = \dfrac{1}{a}[/math] and [math]\left ( a^{-1} \right ) ^{-1} = a[/math].

Strategy: Get rid of those pesky negative powers.
[math]\dfrac{ \left ( x^{-2}y^{10} \right ) ^3 }{ \left ( x^{-4} y z^4 \right ) ^{-5} }[/math]

[math]= \left ( x^{-2}y^{10} \right ) ^3 \left ( x^{-4} y z^4 \right ) ^5[/math]

[math]= \left ( \dfrac{y^{10}}{x^2} \right ) ^3 \left ( \dfrac{yz^4}{x^4} \right ) ^5[/math]

Can you finish?

-Dan
 
topsquark - thanks for the help

following your basic rule really helped out and clarified for us.
 

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