Question 72724
When you are tasked to raise a quantity to the 5th power, what you are being asked to do 
is to write he quantity down 5 times in a row and then put multiplication signs between 
these 5 terms. For this problem this involves:
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{{{(6*10^4)*(6*10^4)*(6*10^4)*(6*10^4)*(6*10^4)}}}
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and by the rules of multiplication you get {{{6*6*6*6*6 = 7776}}} and you multiply the {{{10^4}}} 
terms by adding the exponents to get {{{10^(4+4+4+4+4) = 10^20}}}. Therefore the answer becomes
{{{7776*10^20}}} which can be changed to scientific notation if you wish by taking a factor of
{{{10^3}}} from the 7776 making it {{{7.776 * 10^3}}} and multiplying this by {{{10^20}}}.
In doing so you can add the exponents of the 10s to get the scientific notation form of the
answer as equal to {{{7.776 * 10^23}}}.
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That's the long way of doing it, but it shows how it can be thought of.  The short way
is to think of the original problem as:
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{{{(6^1*10^4)^5}}}
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Then multiply the exponent 5 times each of the 2 exponents in parentheses to get:
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{{{6^5 * 10^20}}}
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and you can raise 6 to the 5th power on any basic scientific calculator ($10 or less) to get
that it is 7776 and multiply that by {{{10^20}}} to get the answer as{{{7776*10^20}}}
and this can again be converted to scientific notation as was explained above.
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Hope this helps you with the rules of exponents.