SOLUTION: I need help with this problem 7^2 ___ 8^8 I come up with 1 _____ 117649 and my friend comes up with 1 ___ 7^6 could you please help me solve this probl

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Question 492030: I need help with this problem

7^2
___
8^8
I come up with
1
_____
117649
and my friend comes up with
1
___
7^6
could you please help me solve this problem?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
7^2 / 8^8 = 49 / 16777216 = .000002921

i don't think there's an easy way to do it other than using your calculator to solve for it.

if it was 7^2 / 7^8, then the base is the same and your friend's answer of 1 / 7^6 would be correct.

unfortunately, the base in the denominator is 8, not 7.

that does not allow the simplification that he performed.

you could make the bases equivalent but that's a lot of work for not very much to be gained.

for example:

7^2 is equivalent to 8^(1.871569948)

your equation then becomes:

8^(1.871569948) / 8^8 which can now be simplified to:

1 / 8^6128430052 which becomes equal to .000002921.

you get the same answer with a lot of extra work involved and you had to use your calculator anyway.

so, you're both wrong for different reasons.

the properties of exponent arithmetic are:

a is the base
x and y are exponents.
the base must be the same for this property to work.

a is the base.
x and y are exponents.
the base must be the same for this property to work.

a is the base.
x is the exponent.

a is the base.
x is the exponent.
in case you can't see it, the exponent is .

here's a link to some of the properties of exponents.

http://www.algebralab.org/studyaids/studyaid.aspx?file=Algebra2_6-1.xml