This isn't a "technical" proof, but let me give you an example that may help you to see why it's true.
Suppose we have (2^2)^3
What is this??
It's just (2*2) * (2*2) * (2*2). In other words, we're just "cubing" (2*2).
But, this is just 2 * 2 * 2 * 2 * 2 * 2 = 2^6 = 2^(2*3)
So, (2*2)^3 = 2^(2*3)
Does that help??
+128408 
