What are the differences of radicals and rational exponents?

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Answer 1 · 2015-06-28T18:46:13

Combined with integer exponentiation, you can express the same things using either notation:

#x^(p/q) -= root(q)(x^p)#

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

If you combine a radical with an integer exponent then you can express the same concept as a rational exponent.

#x^(p/q) -= root(q)(x^p)#

An #n#th root can be expressed as a rational exponent:

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

The differences are basically notational.

Note that this assumes that #x > 0#. If #x <= 0# or is a complex number then these identities do not always hold.