# Thread: Difference between Exponents and Roots

1. ## Difference between Exponents and Roots

I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?

2. ## The Difference is negligable

Hi Math Buddy, welcome to MHF.

The truth is that you can represent any root in the form of an exponent

for example the square root of 2 is also 2 raised to the power of (1/2).

Or SQRT(2) = 2^(1/2)

Math Guru

3. ## Thnk you Math Guru

The teacher was very impressed with my (actually your) answer. She asked my how I knew that and I told her about your forum.

Thanks Math Guru,

Math Buddy

4. Originally Posted by Math Buddy
I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?
none, if you trust in fractionals
Look at this

in natural numbers (0,1,2,3,4...)
x^2=4 means x=2, because 2^2=4

and if I loook for an exponent that gives me

4^x = 2?

How much is x?

not 1 because 4^1 = 4
not 0 because 4^0 = 1

something in between, but how much?
Remember power laws:

(3^4)^5 = 3^20

4^x=2 needs that x is... 0.5!
so 4^(1/2) is the same that sqrt(4), that is 2.

bye

hope this helps

5. I think that the difference between an exponent and a root is that an exponent is a value used as a power to which another value is raised and a root is a number that, when multiplied by itself an appropriate number of times, returns the value under the radical.

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# what is different between root and exponent?

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