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.

Solution Preview

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.

...Advantage: Simplifying radicals is often ... an equation involves manipulation of the exponent of a term, it's helpful to have an exponent instead of a ...

Radicals and Rational Exponents. ... symbol is widely used, converting to rational exponents has advantages. Could you help me understand an advantage of rational ...

Radicals and Rational Exponents. While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational ...

... Explain an advantage of rational exponents over the radical sign. ... Explain an advantage of rational exponents over the radical sign. Advantages. ...

Radicals and Rational Exponents. While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational ...

Radicals and Rational Exponents and Applications of ... widely used, converting to rational exponents has advantages... Explain an advantage of rational exponents over ...

... He was one of the first exponents of the ... 9. Radical theories, also from the 1960s and 1970s ... find out more, including the comparative advantages and weaknesses ...

... segment where there is an exponential growth expected ... enabled mobile phones to gain advantage in the ... have difﬁculty adapting to radical technological change. ...

... uses the "paradigm" notion to explain exponential change ... with the dangers inherent in this radical miniaturization of ... The advantages that they will give to some ...