SOLUTION: how can i simplify by combining like terms? {{{(63^(-2))*(28^5)*7}}}

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Question 77895: how can i simplify by combining like terms?
%2863%5E%28-2%29%29%2A%2828%5E5%29%2A7

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
%2863%5E%28-2%29%29%2A%2828%5E5%29%2A7
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The negative exponent can be changed to a positive exponent if the 63 is moved to a denominator.
This would make the problem:
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%281%2F63%5E2%29%2A%2828%5E5%29%2A7
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Now factor the 63 into %289%2A7%29 and the 28 into 4%2A7. Substitute these into the
expression to get:
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%281%2F%289%2A7%29%5E2%29%2A%28%284%2A7%29%5E5%29%2A7
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by the power rule of exponents, the terms inside the parentheses each get raised to the
power associated with the brackets. This converts the problem to:
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1%2F%289%5E2%2A7%5E2%29%2A%284%5E5%29%2A%287%5E5%29%2A7
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in the numerator multiply the terms containing 7 by adding exponents (remember that 7
is the same as %287%5E1%29) to get:
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1%2F%289%5E2%2A7%5E2%29%2A+%284%5E5%29%2A%287%5E6%29
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divide the 7%5E2 in the denominator into the 7%5E6 in the numerator by subtracting
the exponents to get 7%5E%286-2%29+=+7%5E4. This reduces the problem to:
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1%2F%289%5E2%29%2A+%284%5E5%29%2A%287%5E4%29+=+%28%284%5E5%29%2A%287%5E4%29%29%2F9%5E2
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there are no more factors in the numerator that are common with factors in the denominator.
You could, if you wish, factor the 4 of the first term into the numerator into 2*2 and
the 9 in the denominator into 3*3 to get:
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%28%28%282%2A2%29%5E5%29%2A7%5E4%29%2F%283%2A3%29%5E2 which would expand to:
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%28%282%5E5%29%2A%282%5E5%29%2A7%5E4%29%2F%283%5E2%2A3%5E2%29+
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but that doesn't accomplish much. Or you could multiply everything out to get:
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2458624%2F81
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Hope this helps you to see how to work this problem.
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