SOLUTION: while the radical symbol is widely used, converting to rational exponents has its advantages. Explain an advantage of rational exponents over the radical sign. Include in your ans

Algebra ->  Algebra  -> Radicals -> SOLUTION: while the radical symbol is widely used, converting to rational exponents has its advantages. Explain an advantage of rational exponents over the radical sign. Include in your ans      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 84138: while the radical symbol is widely used, converting to rational exponents has its advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Lets say you had

sqrt%28x%29%2Aroot%283%2Cx%29

how would you simplify this? Well since we have a square root and a cube root, we cannot mix the two expressions. In order to simplify, you would have to raise everything to the 6th power like this:

%28sqrt%28x%29%2Aroot%283%2Cx%29%29%5E6

and simplify

x%5E3%2Ax%5E2

x%5E5

root%286%2Cx%5E5%29=x%5E%285%2F6%29

But simplification gets tricky. However, since this expression is true



We'll have an easier way to simplify. So we can let sqrt%28x%29 become and root%283%2Cx%29 become . So we'll get:

.

This is just one of the many examples where exponent notation is easier to use.