1. Multiplication of Numbers in Index Form

Use your calculator to evaluate: 3²*3³=27*9=243

Compare with 3⁵=243

So, 3²*3³=3⁵

LAW 1: When carrying out multiplication of numbers in index form with the same base, add the powers (index) of the base.

That is: am*an=am+n

2. Division of Numbers in Index Form

3⁶/3⁴=9

Express your answer as a power of 3: 9=3²

Compare with 3²=3⁶/3⁴

LAW 2: Division of numbers in index form, subtract the indices of the denominators from those of the numerators and raise the base to this difference.

That is: an÷am=anam=an-m

3. The Zero Power of a Number

Carry out 3⁶/3⁶=3⁰

LAW 3: When any number except zero (0) is raised to the power zero (0). It is equal to 1.

That is: a0=1 Eg: 100⁰=1

4. When we have to multiply two powers on a single number we multiply the powers.

(am)n=amn

5. a1n=na

a12=a (Square root)

a13=3a (Cube root)

a14=4a (Fourth root)

6. amn=(na)m
7. a-n=1an