SOLUTION: what does it mean to raise a power to a power and how it is related to multiplication. Provide an example to illustrate.

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Question 143755: what does it mean to raise a power to a power and how it is related to multiplication. Provide an example to illustrate.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Raising a power to power means taking a power and raising it to another power.
For instance, %28x%5Ey%29%5Ez means to raise the power x%5Ey to the power z.
How is that related to multiplication?
Let's expand %28x%5Ey%29%5Ez
x^y * x^y * x^y * ... x^y *x^y using x%5Ey as a factor z times.
Now, using the products of powers, we get
x^y * x^y * x^y * ... x^y *x^y = x^(y+y+y+....y+y) (z times)
Which can be written as
x%5E%28yz%29

So a power to a power results in a the base being raised to the product of the two powers.
See this for a good explaination --> http://www.purplemath.com/modules/exponent.htm