rational exponents and radical signs

jayeamy81

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Jun 20, 2006
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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.
 
Whenever you are wanting to know something like this always Google it. I found this exact same question on this board. :shock:
Hopefully it will help: Link
 
jayeamy81 said:
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:
 
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: \(\displaystyle \;\sqrt{x}\,\cdot\,^3\!\!\sqrt{x}\)


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

\(\displaystyle \;\;\sqrt{x}\;=\;^{^6}\!\sqrt{x^3}\)

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

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


(b) With rational exponents, we have:

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