SOLUTION: what is the answer to (x cubed) w/ 5 as the outside exponent

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Question 71974: what is the answer to (x cubed) w/ 5 as the outside exponent
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E3%29%5E5
.
You get the answer to this by multiplying the two exponents to get x%5E%285%2A3%29 which
simplifies to x%5E15.
.
Think of it this way ... when you raise a quantity to the 5th power, you multiply that
quantity times itself until it appears 5 times in the string of multiplications. So what
you are asked to do in this problem is to raise x%5E3 to the 5th power which translates
to:
.
%28x%5E3%29%2A%28x%5E3%29%2A%28x%5E3%29%2A%28x%5E3%29%2A%28x%5E3%29
.
Then in this string you can replace each of the x%5E3 terms by x%2Ax%2Ax and the
result is:
.
%28x%2Ax%2Ax%29%2A%28x%2Ax%2Ax%29%2A%28x%2Ax%2Ax%29%2A%28x%2Ax%2Ax%29%2A%28x%2Ax%2Ax%29
.
and if you count them all up, there are 15 x's in this string ... which translates
to x%5E15.
.
That's why the rule that when you raise an quantity with an exponent to another power you
do so by just multiplying the exponents.
.
Hope this helps you to see a little more about how exponents work.