Consider the following multiplications.

.

Also

.

Try also several calculations like these and observe what happens.

From these calculations, we can observe that

and

or, in general

.

We now, prove our conjecture.

**Theorem:**

**Proof **

If we multiply the expression on the left hand side by itself n times, we have

.

On the other hand, a positive number ab has only a single positive root, .

Therefore,

.

This completes our proof.