What is a rational exponent?

Question

1780 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-11T21:24:22

A rational exponent is an exponent of the form #m/n# for two integers #m# and #n#, with the restriction #n != 0#.

#x^(m/n)# is basically the same as #root(n)(x^m)#

Some general rules for exponents are:

#x^0 = 1#

#x^1 = x#

#x^-1 = 1/x#

#x^a * x^b = x^(a+b)#

#(x^a)^b = x^(a*b)#

If #n# is a positive integer then

#x^(1/n) = root(n)(x)#

From these rules, we can deduce:

#(root(n)(x))^m = (x^(1/n))^m = x^(1/n*m)#

#=x^(m/n)#

#=x^(m*1/n) = (x^m)^(1/n) = root(n)(x^m)#