Is that your work there? Because that looks good to me (so long as we agree that x is positive and that y and z are nonzero).

You are correct when you say that raising a product to an nth power is the same as multiplying that product by itself n times. The result of this is that the power gets "distributed" to each factor. That is, in general,

.

Another useful property is

.

So,

,

again with and .

Edit: But be sure you see that we cannot distribute powers over addition or subtraction. That is, for arbitrary and (though there are specific values for which this will be true). In this case, we would have to multiply by itself times.