SOLUTION: how do you know when to multiply the exponet?

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Question 78647: how do you know when to multiply the exponet?
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You multiply exponents when you raise a variable or a constant to some power.
Here's an example:
%28x%5E2%29%5E3+=+x%5E%282%2A3%29=x%5E6
%283%5E2%29%5E3+=+3%5E%282%2A3%29=3%5E6+=+729
Whenever you multiply variables, then you woul add the exponents only if the variables (also called the base) are the same.
Examples:
%28x%5E2%29%28x%5E3%29+=+x%5E%282%2B3%29 = x%5E5
%284%5E3%29%284%5E4%29+=+4%5E%283%2B4%29 = 4%5E7+=+16384

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets say you have something like
%28x%5E2%29%5E3
This breaks down to

%28x%5E2%29%28x%5E2%29%28x%5E2%29

Now if we multiply this out we get

x%5E%282%2B2%2B2%29=x%5E6

Which is equivalent to

x%5E%282%2A3%29=x%5E6
So this way is much faster since if we had %28x%5E5%29%5E20 we would have to add 5 to itself 20 times. However, we can use multiplication as a shortcut to get to the same answer.

So you multiply exponents when you have an expression with an exponent (like x%5E2) that is raised to another exponent (for instance %28x%5E2%29%5E3=x%5E%282%2A3%29=x%5E6)