Question

Tutorial 1 : INDICES

Answer 1

Consider "a" and "b" are any two rational numbers and "m" & "n" are any two positive integers Then :
Here :
a and b are the base and the exponents are m,n

Rule 1 : a^m x a^n = a^{m+n}
The base is common and the operator is multiplication.
Example : 5^2 X 5^3 = 5^(2+3)


Rule 2 :
Case i) : m>n
a^m / a^n = a ^(m-n)

The base is common so we pull up the denominator giving rise to a^{-n}.
Now,
we end up having a^m X a^(-n) and according to the Rule 1 : a^(m+(-n)) = a^(m-n)

Example : 5^3 / 5^2 = 5^(3-2)
here m : 3 and n : 2 (m>n)



Case ii) : m<n
a^m / a^n = 1 / a^(n-m)

The base is common and since m is not greater than n so we shift the numerator giving rise to a^{-m} in the denominator.
Now,
we end up having a^(-m) X a^n in the denominator and according to Rule 1 : a^(-m+n) = a^(n-m)
So final expression will be : 1/ {a^(n-m) }


Example : 5^2 / 5^3 =1/ 5^(3-2)
here m : 2 and n : 3 (m<n)

Answer 2

rest coming soon lol

Answer 3

Thank you rvc <3

Answer 4

My pleasure sammi <3

Answer 5

but i will do two rules a day i guess i have a lot to do other than this so

Answer 6

What a great Explanation !!!

Answer 7

Nice job. Thank you for sharing this with us. :)

Answer 8

very well explained :D

Answer 9

Interesting.

Answer 10

I approve. That was deep and very mathy! I like it!

Answer 11

Very mathy x'D

Answer 12

nice job man!

Answer 13

Hmm I'll have to do some more reserach into this though to truly understand it.

Answer 14

This is a great explaination

Answer 15

@ಠ_ಠ

Answer 16

¯\_(ツ)_/¯

Answer 17

thanks

Answer 18

Wow thank you