What is an advantage of rational exponents over the radical sign.?

Question

What is an advantage of rational exponents over the radical sign. and an example of an equation easier to solve as a rational exponent rather then a radical sign. (simple)

Answer 1

1.) When you get into situations where you're multiplying exponents, it's can be easier to use a fraction than a radical.

Example:
x^2 * x^(1/2) = x^(5/2) as opposed to x^2 * √x.
or √x^4 = x^2, as opposed to (x^4)^(1/2) = x^(4 * 1/2) = x^2

2.) If you're dealing with cubic roots and beyond, it's generally easier to express as a fraction rather than write a little 3 (or whatever #) on the radical. On computers, you can't write a cube root without a fractional exponent.

I generally use the radical only for square roots.

Answer 2

Rational exponents are in basic terms greater handy to artwork with. the guidelines for using them are in basic terms less complicated and lots greater 'intuitive'. inspect e^(cuberoot(y²)) = y^(5'th root(x^3)) discover y as a function of x. you attempt that with radicals, you will bypass nuts attempting to maintain them promptly. Doug