# Math Help - need help please!

2. Originally Posted by bobby77
I see no advantage. Except it is easier to write.

3. Hello, bobby77!

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?