Solving a Rational exponent(simplify)

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The discussion centers on simplifying the expression c(c^(5/6))/c^2 and converting it to a positive exponent. The initial attempt incorrectly simplifies c(c^(5/6)) to c^(5/6) instead of c^(11/6). The correct approach involves recognizing that c(c^(5/6)) should be combined as c^(1 + 5/6), resulting in c^(11/6). When dividing by c^2, the exponents are subtracted, leading to a final expression of 1/c^(1/6). The confusion arises from misapplying exponent rules during 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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