2008
Sun
27
Apr
Sergeant Loi avatar

Sergeant Loi’s Mid-Year Boot Camp 2008 – Obey The Rules of Indices!

(8)
Tuition given in the topic of A-Maths Tuition Notes & Tips from the tuition centre desk of Sergeant Loi at 1:58 am (Singapore time)
Sergeant Loi

No one messes around with Sergeant Loi!

The Mids are just around the corner. A time when students are put through grueling tests to realize how little they’ve actually learnt in a semester dominated by fun and laughter, peace and joy.

Unfortunately in this critical time, no word has yet been heard from Miss Loi – who is presumed to be still trapped in that fitting room since a few days ago.

And so to fill this void …

*Puts on helmet*

*SHOWS STERN & MEAN FACE*

Ok boys and girls, this is Sergeant Loi sent by The Temple to maintain discipline in Miss Loi’s absence!

In the coming days, you shall be subjected to a series of no-nonsense DRILLS and exercises on several ‘Hot Topics’ that you MUST complete in order to survive your Mids!

Rest assure that, with the menacing taskmaster Sergeant Loi around, there shall be no silly stories, lame content and fooling around on this blog, for she is not as cheong hei as the Sexy Maths Tutor there is no time to lose if you want to pass your Mids!

*Sounds bugle*

EVERYBODY FALL IN! Sergeant Loi’s first drill with you shall be on Indices!

*Cracks whip*

The Rules of Indices

A. SIMPLIFY THOSE WITH INDICES 1 OR 0

i.e. a^0 = 1, a^1 = a duuuuh!

B. FOR THE SAME BASE (a) WITH DIFFERENT INDICES (m,n): MULTIPLY IS TO PLUS, DIVIDE IS TO MINUS, POWER IS TO MULTIPLY

  1. a^m*a^n = a^{m+n}
  2. {a^m}/{a^n} = a^{m-n}
  3. (a^m)^n = a^{mn}

Attention! ONLY for the same base (i.e. a)! DON’T ever do this: a^m*b^n = (ab)^{m+n} → WRONG!

C. THOSE WITH COMMON INDICES CAN BE MARRIED

  1. a^n*b^n = (ab)^n
  2. {a^n}/{b^n} = (a/b)^n

Attention! ONLY for those with same indices (i.e. n)! Couples with different indices cannot get along!

D. INDICES GET INVERTED WHEN TRANSFERRED TO THE OPPOSITE SIDE

e.g.

  1. a^{1/3} = b doubleright a = b^3
  2. a^{-1/3} = b doubleright a = b^-3
    (The negative (-) sign follows across to the other side!)
  3. a^{-3/2} = b doubleright a = b^{-2/3}
    (The index gets inverted on the other side!)

SAMPLE PRACTICE QUESTION

If (3^{x+2})(5^{x-1}) = 15^{2x}, find the value of 15^x.

Ans:

doubleright (3^x * 3^2)({5^x}/{5^1}) = 15^{2x} → using B(1)+B(2) above
doubleright (3^x * 5^x)(9/5) = 15^{2x}
doubleright {15^x}(9/5) = 15^{2x} → using C(1) above
doubleright 9/5 = {15^{2x}}/{15^{x}} = 15^{2x-x} = 15^x → using B(2) above

Get these rules drilled into your head! Spot the pointers and common mistakes in red! Understand the representative sample question! Check out this question for further practice!

Print this out if necessary and obey the above rules strictly – for if you don’t and end up fumbling in your exams Sergeant Loi will throw you to the deepest dungeons beneath The Temple where unspeakable miseries shall be heaped upon you!

*Cracks whip!*

N.B. On the other hand, if you have any valuable input to add to the notes above, you might even get a medal from Sergeant Loi for your contributions!

頑張って!!!

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

  1. Leave A Comment!
Comments & Reactions

8 Comments

  1. krisandro's Avatar
    krisandro commented in tuition class


    2008
    Apr
    27
    Sun
    2:23am
     
    1

    OooOoo.... whip!

    *looks at Sergeant Loi and winks*

    Are there students reading this? I mean.. reallllly young ones? 😀

  2. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    27
    Sun
    8:16pm
     
    2

    Wah... a powerful authority figure.....

    I know some people would like that... *wink*

  3. Sergeant Loi's Avatar
    Sergeant Loi commented in tuition class


    2008
    Apr
    27
    Sun
    10:32pm
     
    3

    Those of you who just winked at Sergeant Loi KNOCK IT DOWN TWENTY!!!

  4. FoxTwo's Avatar
    FoxTwo commented in tuition class


    2008
    Apr
    28
    Mon
    8:03am
     
    4

    uh, what's "it"? Why do you want to knock it down anyway?

  5. Sergeant Loi's Avatar
    Sergeant Loi commented in tuition class


    2008
    Apr
    28
    Mon
    2:30pm
     
    5

    Still ask so many questions?! TEN MORE PUSH-UPS FOR YOU!!!

    Try to be funny again and you'll be further punished with 10x push-ups - where x = no. of silly questions asked!

  6. tohkiatshengKEN's Avatar
    tohkiatshengKEN commented in tuition class


    2008
    May
    1
    Thu
    2:19pm
  7. mel's Avatar
    mel commented in tuition class


    2009
    Dec
    29
    Tue
    6:44pm
     
    7

    what happens if the power is a fraction or a negative fraction ?

  8. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2010
    Jan
    18
    Mon
    12:20am
     
    8

    mel: Miss Loi is glad that you asked this question (about fractional indices) dear 😀

    When we have something like a^{-{m/n}}:

    1. The denominator n of the power represents the nth-root of a e.g. 2^{1/3}=root{3}{2}
    2. The negative sign in the power (regardless of whether it's a fraction or whole number) ⇒ the inverse of a (to the equivalent positive power) e.g. 2^{-1/3}=1/{root{3}{2}}

    So as an e.g. to sum it up further, 2^{-2/3}=1/({root{3}{2}})^2

    Use your calculator to check if the above can be written as 1/{root{3}{2^2}} as well? 😉

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