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What is the advantage of using exponents rather than radicals?

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. What is an example of an equation easier to solve as a rational exponent rather than as a radical sign.

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The advantage is: rational exponents are much easier to work with than are radical signs since we can manipulate them with simple arithmetic operations. For example, let's look at the following equation:

(sqrt(3x+1))^3 = 64

Got that? That means that (3x+1) is in a radical sign and the whole thing is cubed. Remember, the "^" sign means "raised to the power of."

How can we solve this? Well, if we get rid of the radical sign, it ...

Solution Summary

I provide a solution to this problem that illustrates that it is much easier to solve an algebraic equation using rational exponents than it is using the radical sign.