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

Calculations can be made much more easily using rational exponents. To multiply two numbers, you simply add the exponents. To divide two numbers, you subtract the exponents.

For example:
3^1/3 * 3^1/4 = 3^(1/3+1/4) = 3^(7/12)

It would be very difficult to perform this calculation using the radical sign.

Answer 2

Rational exponents are just easier to work with. The rules for using them are just simpler and much more 'intuitive'.

Look at
e^(cuberoot(y²)) = y^(5'th root(x^3)) Find y as a function of x. You try that with radicals, you'll go nuts trying to keep them straight.

Doug

Answer 3

it extremely is an equation, substitute all the exponents to a thorough sign. It gets messy. additionally, it is not time-honored to apply the novel sign different than with the numbers 2 or 3. What in case you have been going to apply the basis 2x-y? you will get to that later on your math classes (((((2x+3)^.25)+x^3 -4X)^.75)-3x^7+5x^2)^.5

Answer 4

x^(2/3)*x^(3/4)=x^(3/4+4/5) rational exponents
cube root of x^2+4th root of x^3 radical