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Math Help - indices (i think)

  1. #1
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    indices (i think)

    hi this is my question:

    (5^3)^2 X 25^2

    i have no idea how to do this
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  2. #2
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    Quote Originally Posted by andyboy179 View Post
    hi this is my question:

    (5^3)^2 X 25^2

    i have no idea how to do this
    5^6 \times 5^4 = 5^{10} = 9 765 625
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  3. #3
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    Quote Originally Posted by andyboy179 View Post
    hi this is my question:

    (5^3)^2 x 25^2

    i have no idea how to do this
    Do you want to solve (5^3)^2 \times 25^2 and get a numeric solution?

    (5^3)^2 = 5^{3\times 2} = 5^6

    Also note that 25 = 5^2, this means that 25^2 = (5^2)^2 = 5^4.

    Following through with what I've done above, can you get (5^3)^2 \times 25^2 in terms of 5^n, where n is just an integer (whole number) ?
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  4. #4
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    thank you very much for answering!!!

    how would i work out 25^3 divided by 5^-4?
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  5. #5
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    Quote Originally Posted by andyboy179 View Post
    thank you very much for answering!!!

    how would i work out 25^3 divided by 5^-4?
    Use what I said above to get 25^3 in terms of 5^n.

    Also notice that 5^n \times 5^m = 5^{n+m}.

    This also applies for division, \frac{5^n}{5^m} = 5^{n-m}.

    Another thing, do not just post questions and hope for the answer, show us your working so far and where you have got stuck, then we can help you.
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  6. #6
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    Quote Originally Posted by craig View Post
    Use what I said above to get 25^3 in terms of 5^n.

    Also notice that 5^n \times 5^m = 5^{n+m}.

    This also applies for division, \frac{5^n}{5^m} = 5^{n-m}.

    Another thing, do not just post questions and hope for the answer, show us your working so far and where you have got stuck, then we can help you.

    would 25^3= 5^6?

    and could you explain what to do on 5^-4???
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    Quote Originally Posted by andyboy179 View Post
    would 25^3= 5^6?
    Yes

    and could you explain what to do on 5^-4???
    Recall that for a^{-b} = \frac{1}{a^b}
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  8. #8
    Super Member craig's Avatar
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    Quote Originally Posted by andyboy179 View Post
    would 25^3= 5^6?
    Correct!

    Quote Originally Posted by andyboy179 View Post
    and could you explain what to do on 5^-4???
    Use the fact that \frac{5^n}{5^m} = 5^{n-m}, just remember that it's a minus 4 you are using, not 4.
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  9. #9
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    5^-4= -25^-2 ???
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  10. #10
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    Quote Originally Posted by andyboy179 View Post
    5^-4= -25^-2 ???
    Not quite, the exponent is fine but consider the sign on 25^{-2}
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  11. #11
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    Quote Originally Posted by e^(i*pi) View Post
    Not quite, the exponent is fine but consider the sign on 25^{-2}

    so would i just be -25^2
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  12. #12
    Super Member craig's Avatar
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    \frac{25^3}{5^{-4}}

    \frac{5^6}{5^{-4}} = 5^{6-(-4)} = ??
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  13. #13
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    Quote Originally Posted by craig View Post
    \frac{25^3}{5^{-4}}

    \frac{5^6}{5^{-4}} = 5^{6-(-4)} = ??

    what so i leave 56-4 the same and then do the divide part?

    would it = 5^10
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  14. #14
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    Quote Originally Posted by andyboy179 View Post
    what so i leave 56-4 the same and then do the divide part?

    would it = 5^10
    Yes. When multiply or dividing just remember the two rules above. It doesn't matter what the base numbers are, (5 or 25), as long as they are the same.

    Hope this has helped, be sure to post again if there's anything you stuck on
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  15. #15
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    thankyou so much for all of the help!!!
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