rational exponent versus radical sign

[VincentsEcho]

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.

 

[Denis]

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

Thanks Vincent; I'll make sure I remember that. :idea:

 

[soroban]

Hello, VincentsEcho!

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

It is <u>very</u> difficult to combine: \(\displaystyle \,(\sqrt{x})(\sqrt[3]{x})\)

With rational exponents, we have: \(\displaystyle \L\,x^{\frac{1}{2}}\cdot x^{\frac{1}{3}}\:=\: x^{(\frac{1}{2}+\frac{1}{3})}\;=\; x^{\frac{5}{6}}\;=\;\sqrt[6]{x^5}\)