Rules of Exponents (4)^(1/5) * (4)^(1/5)

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    Exponents Rules
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Discussion Overview

The discussion revolves around the rules of exponents, specifically examining the expression (4)^(1/5) * (4)^(1/5) and its simplification. Participants explore the equivalence of different forms of the result, including 4^(2/5) and 2^(4/5).

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the expression (4)^(1/5) * (4)^(1/5) and suggests it simplifies to 4^(2/5).
  • Another participant agrees with the simplification and questions the relationship between 4^(2/5) and 2^(4/5).
  • A further participant asserts that both forms represent the same value, drawing a parallel to the equivalence of 2^4 and 4^2.
  • One participant points out that since 4 can be expressed as 2^2, the equivalence of 4^(2/5) and 2^(4/5) can be demonstrated through exponent rules.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the simplifications and the equivalence of the two forms, though there is some exploration of how both can be seen as correct.

Contextual Notes

The discussion does not delve into potential limitations or assumptions regarding the definitions of exponents or the context in which these expressions are used.

Who May Find This Useful

This discussion may be useful for individuals interested in understanding the rules of exponents and the relationships between different exponential forms.

mathdad
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Rules of Exponents

(4)^(1/5) * (4)^(1/5)

4^(1/5) + (1/5)

4^(2/5)

Correct?

Is the answer 2^(4/5)?
 
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Yes, everything you posted is correct. (Yes)
 
MarkFL said:
Yes, everything you posted is correct. (Yes)

What is the difference between 4^(2/5) and 2^(4/5) as the answer?

How can both answers be correct?
 
RTCNTC said:
What is the difference between 4^(2/5) and 2^(4/5) as the answer?

How can both answers be correct?

They are just different form for the same number...just like 2^4 and 4^2 can both represent 16. :D
 
I hope that you know that 4= 2^2! So 4^{2/5}= (2^2)^{2/5}= 2^{4/5}.
 
Thank you everyone.
 

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