Dear Ms Wong, This new blog will be completely from what i learn. None of them is from the internet, except for pictures. Thank you.



Indices

Some rules are easy to remember , however, students normally forget to spot the following two rules. When doing indices, the key is to remember to apply the correct rule to simplify the expression involving indices.

1. 1/(a^-n) = a ^n
   

For this rule. Students tend to forget the rule because of the negative sign. Students tend to forget that it can be changed to the positive sign.


For example, when 1/ (8^-2) , students will forget the rule. Instead , they will think in the sense how to make the 8^-2 into positive 8^2.

2. a^m / b ^m = (a/b) ^m


For this rule. students tend to mix it up with a^m / a^n = a ^m-n. Hence they are unsure if they can combine together when not same base but the same power.

The easier way to remember this rule is to remember that the multiply and divide rule works on both same base and same power .


Quick test ( common mistakes )

1. 2^3 times 3 ^2 = 6 ^3+2
   

Is this question correct?

Ans: If you say yes you are wrong. Also, the reason why you are wrong is because you forget the rule that in multiplication, the base of the power has to be equal before we can add up the bases.


2. 2^2+ 2^3 = 2 ^2 + 3

Is this equation equal? Many students will add up the power because they misread the question and used the a^m times a ^n = a ^m+n .

Ans: The equation is not equal. The key lies in the + sign! Only when it is multiplication or division and the base is the same can the power of the indices be added up.


3. Is 0 a integer? Positive or negative?

Students have the impression that 0 has no value and is not a integer.

Ans: 0 is a integer. However students please take note that 0 is neither a positive integer nor a negative integer.


4. 2 ^9x = 1 / 2048


For students who know their rules well they will know what to do. However as i previously mentioned, the 1/(a^-n) = a ^n rule is often forgotten


Ans: 2 ^9x = 2048 ^-1 Using 1/(a^-n) = a ^n rule...
2^9x = 2 ^11 (-1)
x = - 1 / 2/9.

5. 8 ^ 5x = 32 ^ x-3 is it equal to 8 ^5x times= (2 ^5 ) ^x-3?


The misinterpretation is that 2 ^5 is 32 . However when it is power with another indices. This is wrong.


Ans : 8^5x = 2 (16) ^x-3
= 2 ( 2^4 ) ^x-3


This is the way the problem is solved by reducing it to 16 first. Only then can we use the indices rule.