rational exponents and radical signs

[jayeamy81]

Can someone explain the advantage of using rational exponents over the radical and sign or at least show an example of the difference so i can see the advantage.

[jonboy]

Whenever you are wanting to know something like this always Google (http://www.google.com/search) it. I found this exact same question on this board. :shock:
Hopefully it will help: Link (http://www.freemathhelp.com/forum/viewtopic.php?p=42489&highlight=&sid=e8164aa0909dd0925a591680df777056)

[Denis]

Can someone explain the advantage of using rational exponents over the radical and sign or at least show an example of the difference so i can see the advantage.
Your question makes no sense...can you rewrite it, with an example :idea:

[soroban]

Hello, jayeamy81!


Can someone explain the advantage of using rational exponents over the radical sign?
Or at least show an example of the difference, so i can see the advantage.
Simplify: \;\sqrt{x}\,\cdot\,^3\!\!\sqrt{x}


(a) It can be done with radicals . . . like this:

\;\;\sqrt{x}\;=\;^{^6}\!\sqrt{x^3}

\;\;^3\!\sqrt{x}\;=\;^{^6}\!\sqrt{x^2}

The problem becomes: \:^{^6}\!\sqrt{x^3}\,\cdot\,^{^6}\!\sqrt{x^2}\;=\; ^{^6}\!\sqrt{x^3\cdot x^2}\;=\;^{^6}\!\sqrt{x^5}


(b) With rational exponents, we have:

\;\;\sqrt{x}\,\cdot\,^3\!\sqrt{x}\;=\;x^{^{\frac{1 }{2}}}\cdot x^{^{\frac{1}{3}}}\;=\;x^{^{\frac{1}{2}+\frac{1}{3 }}}\;=\;x^{^{\frac{5}{6}}}