Solving a Rational exponent(simplify)

[DPXJube]

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.

 

[SammyS]

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 c^11/6 .
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.

 

[DPXJube]

Could you explain to me where exactly that fraction came from?

 

[SammyS]

1 + 5/6 = 11/6

 

[HallsofIvy]

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(c^5/6)= c^5/6 if and only if c= 1.
c¹c^5/6= c^{1+ 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.