While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage

Question

While the radical symbol is widely used, converting to rational exponents has 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 1

The easiest answer is because if you're multiplying different exponents, it's easier to multiply the exponents than it is to try to muliply radicals.

√3 * 3√3 * 4√3 is not as easy to work with as:
3^(1/2) * 3^(1/3) * 3^(1/4) = 3^(1/2 * 1/3 * 1/4) = 3^(1/24).

Answer 2

Here is an equation, change all the exponents to a radical sign.
It gets messy. Also, it is not customary to use the radical sign other than with the numbers 2 or 3. What if you were going to use the root 2x-y? You will get to that later in your math courses

(((((2x+3)^.25)+x^3 -4X)^.75)-3x^7+5x^2)^.5

Answer 3

Exponents are easier to type without special fonts, for example by using "^" to mean exponentiation.

Answer 4

for one it rather is much less bulky, yet i think of the actual benefit is you could cut back extra truthfully. 450root(x^225) = x^(225/450)= x^a million/2 additionally it rather is trouble-free to maintain song with the aid of fact while shifting exponent up and down fractions or to distinctive factor of equation all they do is replace signs and indicators. sqrt(x)=y -> x^a million/2=y -> a million = y*x^-a million/2 a million/a million/a million/sqrt(x) = a million/a million/x^-a million/2 = a million/x^a million/2 = x^-a million/2 and ultimately it rather is stable for calculus and taking a derivative with the aid of fact the set of rules for doing such is trouble-free by-product(x^a million/2) = a million/2*x^-a million/2