See correction in red.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.
Well, those are "relevant equations"!DPXJube said:Homework Statement
Simplify. Write as positive exponent
c(c^5/6)/c^2
Homework Equations
None really, just exponent laws.
What?? c(c5/6)= c5/6 if and only if c= 1.The Attempt at a Solution
c(c^5/6) comes out as...
c^5/6
That's a very strange statement! Dividing the numbers requires subtracting the exponents.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.
A rational exponent is an exponent that is a fraction, where the numerator represents the power to which the base is raised, and the denominator represents the root to be taken.
To simplify a rational exponent, you can rewrite it as a radical expression. For example, x^(3/2) can be written as the square root of x cubed (x^(3/2) = √x^3).
A rational exponent and a radical expression both involve taking roots, but a rational exponent includes a power in addition to the root. For example, x^(3/2) is a rational exponent, while √x^3 is a radical expression.
Yes, you can simplify a rational exponent even if the exponent is negative. You can use the power rule to rewrite the exponent as a positive fraction, then simplify it as normal.
Some common mistakes to avoid when simplifying rational exponents include forgetting to apply the power rule, confusing the numerator and denominator of the exponent, and not simplifying the radical expression completely.