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?
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)
But this may be a more advanced answer for middle school. Does it answer your question?
none, if you trust in fractionalsOriginally Posted by Math Buddy
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.
hope this helps
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.