need help please!

**bobby77** · July 14th 2006, 09:03 AM

explain the advantage of using rational exponents over the radical sign?

**ThePerfectHacker** · July 14th 2006, 09:04 AM

Originally Posted by bobby77

explain the advantage of using rational exponents over the radical sign?

I see no advantage. Except it is easier to write.

**Soroban** · July 14th 2006, 09:30 AM

Hello, bobby77!

Explain the advantage of using rational exponents over the radical sign?

Try this problem: . $\sqrt{x}\cdot\sqrt[3]{x}$

Since $\sqrt[n]{a}\cdot\sqrt[n]{b} \:= \:\sqrt[n]{ab}$ , the two factors must have the same root.

We perform some gymnastics: . $\begin{array}{cc} \sqrt{x} \:=\:\sqrt[6]{x^3}\\ \sqrt[3]{x} \:= \:\sqrt[6]{x^2}\end{array}$ . . . did you follow that?

. . and the problem becomes: . $\sqrt[6]{x^3}\cdot\sqrt[6]{x^2} \:=\:\sqrt[6]{x^5}$

With rational exponents: . $\sqrt{x}\cdot\sqrt[3]{x}\:=\:x^{\frac{1}{2}}\cdot x^{\frac{1}{3}}\:=$ $\:x^{(\frac{1}{2}+\frac{1}{3})} \:= \:x^{\frac{5}{6}}$

Which way do you prefer?

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need help please!