Rules of Indices



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35 Responses

  1. Stephen Yau says:

    Thanks for this, very helpful stuff

  2. Amy says:

    HELP!!!! I need to know what rule five is for a test tomorrow!! It says in my book:
    2(in powers) -3=1 over 2, to the power 3= 1 over 8??? can
    someone explain please?????

  3. admin says:

    Sorry, I could not get to your comment in time. I will be updating this entry with more content very soon.

  4. it is kind of unclear of how the rules are divided and explained because i think they are more rules. so that was kind of unclear.

  5. whitney says:

    what is A raise to the power x or A raise to the power 2x .

  6. Anna says:

    A very helpful explanantion – thank you.

    In the last line of rule four (just over the rule five title) am I right in thinking that the first fraction has been (inadventently) turn over again?

  7. Emmi says:

    my mind is fully clear after seeing this. thankyou.

  8. segun says:

    Thanks for dis!!!!

  9. ZP says:

    Really helpful. Cheers

  10. Anaan says:

    Hey I need help.
    How do you solve 3 to the power of 100 times 4 to the power of 100?

  11. Author says:

    Hi is that

    [ 3^{100} × 4^{100} ]

    Remember you cannot apply any rule here since the bases for both numbers is different.

  12. Rhyan says:

    thanks this really helps when trying to revise

  13. Lamin Jammeh says:

    Thanks…How does the rule apply when adding or subtracting the same bases but powers eg. X^a + X^b

  14. Bob says:

    Because its brackets basic multiplication and division they ARRRREEE the 3 rules though. :D

  15. YOLO says:

    quite good

  16. saran says:

    how to solve
    10^n – 4^n / 5^n – 2^n

  17. Rasad says:

    this is very help full web but i cant find the quation’s like
    a1 over 2 x a-3 over 4

  18. Rasad says:

    this is very help full web but i cant find the quation’s like this one
    a1 over 2 x a-3 over 4

  19. Thomas Graham says:

    Hi most of your notes i find easy to understand but below my teacher (i’m an adult learner)he as given us stuff to reduce to a single index i have brackets within in brackets and fractions inside that and powers i’m confused have you a page i can look at please?

    • Author says:

      Hello Thomas,

      Can you type some examples of the questions that your teacher wants you to work out. Brackets means multiply so you might have to expand the expressions first. Are they similar to this:
      [(x^2y^3) ÷ (x^2y^4) ]
      [ (4^2(4×4×4)) × ((4×4×4)4^5) ]
      Remember indices rules only apply when the base for all the terms is the same to be able to reduce it to a single indexed number.

  20. Ann says:

    Hi, I am having difficulty working out this question. Can anybody help ?


    The answer is 1/5 but I am having trouble getting to that answer.

    • Chris says:

      Probably not a problem still but thought i would answer anyway. times both sides by three cancels the division on both sides, adding 1 to both sides cancels the -1 on the right side and then you have 11= x

  21. arjun sarkar says:

    i like mathematics

  22. Della says:

    Hi when a – number multiplyed by a – number does the answer become a + number.

  23. Della says:

    Hi when a – number multiplied by a – number does the answer become a + number.

    • Author says:

      Yes. A negative number times a negative number is always equal to a postive number. For example;
      [-2 times -2 = 4]
      [-4 times -4 = 16]
      [-1 times -1 = 1]

  24. this really helps when studying …..thank you :)

  25. amanda says:

    what is the value of o2?
    what is the value of 0-2?
    what is the value of 00?

  26. Barry says:

    3^(x) X 2^(2x-3)=18

    Can any body help me with this question I need to solve for X

    It reads 3 to the power (x) multiplied by 2 to the power of (2x-3) = 18

    Any help greatly appreciated


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