 Chapter 8: Indices By: Yeon

Task  Chapter 8  Section A, B, C Read and make your own notes on PowerPoint Be ready to explain to Mrs. Taher on Monday

Algebraic Products and Quotients in Index Notation (Section A) When simplifying an algebraic equation that has powers, you expand them. So that you can simplify them. For example:  a 2 × a 2 = (a × a) × (a × a) = a 4 d 2 × d 3 × d = (d × d) × (d × d × d) × d = d 5 But, The algebraic numbers or expressions have to be the same for this situation to be possible

Algebraic Products and Quotients in Index Notation (Section A) Whereas when getting products that have numbers before the algebraic letter or squares out of brackets, you also expand, but they are slightly more complex (more rules):  (s 2 ) 3 = s 2 × s 2 × s 2 = s × s × s × s × s × s = s 6 (4y 2 ) 3 = 4y 2 × 4y 2 × 4y 2 = 4 × y × y × 4 × y × y × 4 × y × y = 64y 6

Algebraic Products and Quotients in Index Notation (Section A) When dividing the algebraic numbers (simply put, you cross out the number of algebraic until there’s none left, on one half:

Index Laws (Section B) This makes everything so much easier, simpler, most of all quicker:  2 4 × 2 2 = = 2 6 With algebraic numbers you end up stopping here, but when using whole numbers you can: = 12 (simplify fully)

Index Laws (Section B) You can also do division using subtraction. The same thing applies to this the numericals can be fully simplified, when algebra can only be talken far as shown (in this case, at least):

Index Laws (Section B) For when you use brackets:  (r 5 ) 2 = r 5×2 = r 10 (2 2 ) 4 2 2×

Index Laws (Section B) For when these numbers start to increase in quantity and size index laws are useful:  10hk 3 × 4h 4 = 4 × 10 × h × h 4 × k 3 = 40 × h 5 × k 3 = 40h 5 k 3

Index Laws (Section B)  These index laws make everything so much simpler. We don’t have to do the whole expand and simplify process. You can just do the subtraction, addition, or multiplication of the squared numbers.

Expansion Laws (Section C)  (xy) 3 = x 3 y 3 But when adding numbers in front of algebraic numbers  (5ab) 3  5 3 × a 3 × b 3 = 15a 3 b 3

Expansion Laws (Section C)  When having numerical values with algebra you cannot simplify it to the exact number:

Section A+B+C  Section A discussed the long ways of doing the algebraic indices  Whereas section B stated the shortcut/easier/quicker/and simpler way of doing the indices (which is why it is so much more preferable)  In section C there were more and continuous work, but they didn’t have additional information about the laws etc. So I decided to stop there.