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.