Tuesday, 22 July 2008

Laws of Indices Explained

"What is Indices?" the novice to this maths topics asked.

"They are nothing but numbers with flying numeric powers!" said the maths teacher.

Here I move forward explaining the details of Indices.

Sit back and relax.......

Format of Indices is ax = y.
NOTE: The power "x" should be written small.

There are three basic Laws of Indices:

1) Product Law of Indices

an x am = a (n + m)

Example: a3 x a2 = a 5

2) Quotient Law of Indices

an / am = a(n-m)

Example: a7 / a2 = a(7-2) = a5

3) Power Law of Indices

(an)m = anm

Example: (a2)4 = a8

(a / b)n = an / bn

Example: (K / Y)2 = K2 / Y2

The above are Laws that any maths students must know. However, these laws also produce sub-laws (special laws) from them. See below.

Special Laws of Indices:

  • a0 = 1

  • 1 / an = a-n

The 2 special laws stated above are nothing new. They only have their variable replaced with the number 0, and 1 to extract commonly used operation.




Anonymous said...

good site, although i needed four basic indices

Anonymous said...

nicely explained! please try to give detailed explanation for 'Special Laws of Indices'.


Anonymous said...

wow, i never once needed help with math till this moment, very nice site, it really helped me understand what i didnt, thank yovery much.

Anonymous said...

what about fractional indices??

EeHai said...

Fractional indices involve "roots" of a variable.

If the index is "half" or (1/2), the operation is square root of the variable.
If the index is (1/3), the operation is cube root of the variable.