Solving a Rational exponent(simplify)

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Homework Help Overview

The problem involves simplifying an expression with rational exponents, specifically the expression c(c^5/6)/c^2, and rewriting it with positive exponents.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of exponent laws, particularly the process of combining exponents through multiplication and division. There are attempts to clarify the correct simplification steps and the reasoning behind the results. Questions arise regarding the origin of specific fractions and the validity of certain statements related to exponent manipulation.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the exponent rules and questioning the correctness of initial attempts. Some guidance has been offered regarding the proper handling of exponents, but no consensus has been reached on the correct approach to the problem.

Contextual Notes

Participants note that there are no specific equations provided beyond general exponent laws, and there seems to be confusion regarding the assumptions made in the simplification process.

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Homework Statement


Simplify. Write as positive exponent

c(c^5/6)/c^2


Homework Equations


None really, just exponent laws.


The Attempt at a Solution


c(c^5/6) comes out as...
c^5/6
Dividing exponents requires subtracting them so...
5/6 - 2/1
Find common denominator...
5/6 - 12/6
Equals
-7/6
Turning the whole thing into
c^-7/6

This is completely wrong though as the answer is apparently

1/c^1/6
I would like to know how one comes to this conclusion please.
 
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DPXJube said:

Homework Statement


Simplify. Write as positive exponent

c(c^5/6)/c^2


Homework Equations


None really, just exponent laws.


The Attempt at a Solution


c(c^5/6) comes out as...
c^5/6 ⟵ This should be c11/6 .
Dividing exponents requires subtracting them so...
5/6 - 2/1
Find common denominator...
5/6 - 12/6
Equals
-7/6
Turning the whole thing into
c^-7/6

This is completely wrong though as the answer is apparently

1/c^1/6
I would like to know how one comes to this conclusion please.
See correction in red.
 
Could you explain to me where exactly that fraction came from?
 
1 + 5/6 = 11/6
 
DPXJube said:

Homework Statement


Simplify. Write as positive exponent

c(c^5/6)/c^2


Homework Equations


None really, just exponent laws.
Well, those are "relevant equations"!


The Attempt at a Solution


c(c^5/6) comes out as...
c^5/6
What?? c(c5/6)= c5/6 if and only if c= 1.
c1c5/6= c1+ 5/6

Dividing exponents requires subtracting them so...
That's a very strange statement! Dividing the numbers requires subtracting the exponents.

5/6 - 2/1
Find common denominator...
5/6 - 12/6
Equals
-7/6
Turning the whole thing into
c^-7/6

This is completely wrong though as the answer is apparently

1/c^1/6
I would like to know how one comes to this conclusion please.
 

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