What's the Deal with A^-1/B^-1?

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Discussion Overview

The discussion revolves around the expression A^-1/B^-1 and its simplification. Participants explore the mathematical properties of negative exponents and the implications of dividing by fractions, with a focus on algebraic manipulation.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that A^-1/B^-1 can be simplified to (1/A)/(1/B), indicating a method for handling negative exponents.
  • Others propose that the expression can be rewritten as B/A, emphasizing the process of inverting and multiplying fractions.
  • A participant questions the necessity of obtaining positive exponents in the numerator and denominator before proceeding with simplification.
  • There is a suggestion that the expression is not difficult to understand if approached correctly.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the simplification, indicating that multiple views remain on how to interpret and manipulate the expression A^-1/B^-1.

Contextual Notes

Some assumptions about the properties of exponents and the rules for dividing fractions are present but not explicitly stated, leading to potential ambiguity in the discussion.

Gringo22
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A ^ - 1 / B ^ - 1

:zzz:
 
Mathematics news on Phys.org
B/A Isn't so hard if you think about it.
 
(A/B)^-1? what's the question?
 
You have to get a positive exponent in the numerator and denominator first, right ?
 
A ^ - 1 / B ^ - 1
Can be written ?

(1/A^1) / (1/B^1)
 
yes, what's wrong with it?
 
Gringo22 said:
A ^ - 1 / B ^ - 1
Can be written ?

(1/A^1) / (1/B^1)

Yes, A-1/B-1= (1/A)/(1/B). And to divide by a fraction, you invert and multiply: (1/A)(B/1)= B/A just as in the first response.
 
That you very much. :cool:
 

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