SOLUTION: (6*10^4)^5

Question 72724This question is from textbook McDOUGAL Littell/Houghton Mifflin Algebra 1 An Intergrated Approach
: (6*10^4)^5 This question is from textbook McDOUGAL Littell/Houghton Mifflin Algebra 1 An Intergrated Approach

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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:
.

.
and by the rules of multiplication you get and you multiply the
terms by adding the exponents to get . Therefore the answer becomes
which can be changed to scientific notation if you wish by taking a factor of
from the 7776 making it and multiplying this by .
In doing so you can add the exponents of the 10s to get the scientific notation form of the
answer as equal to .
.
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:
.

.
Then multiply the exponent 5 times each of the 2 exponents in parentheses to get:
.

.
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 to get the answer as
and this can again be converted to scientific notation as was explained above.
.
Hope this helps you with the rules of exponents.
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