1. Laws of exponents

2. Introduction am x bm = (a x b)m am x an = am+n am ÷ an = am-n
If the base is same then we
Add/Subtract the powers
keep the same base.
If the power is same then we
Multiply / Divide the base
keep the same power.
Same Power
Same Base
am x bm = (a x b)m
Same Power m
am x an = am+n
Same Base a
am ÷ an = am-n
Same Base a
Same Power m

3. Examples for whole numbers: 23 x 33 23 ÷ 33 26 x 25 26 ÷ 25
By Applying the rule,
am x bm = (a x b)m
Multiplying the base
Same power (3)
By Applying the rule,
23 x 33 = (2x3)3
By Applying the rule,
Dividing the base
By Applying the rule,
Same power (3)
By Applying the rule,
am x an = am+n
Adding the powers
By Applying the rule, 26 x 25 = 26+5 = 211
Same base(2)
By Applying the rule,
am ÷ an = am-n
Subtracting the powers
By Applying the rule, 26 ÷ 25 = 26-5 = 21
Same base(2)

4. Examples for algebraic terms with negative powers: m-5 x n-5 m-5 ÷ n-5 m-5 x m-2 m-5 ÷ m-2
By Applying the rule,
am x bm = (a x b)m
Multiplying the base
By Applying the rule,
m-5 x n-5 = (m x n)-5
Same powers(-5)
By Applying the rule, Dividing the base
By Applying the rule,
Same powers(-5)
By Applying the rule,
am x an = am+n
Adding the powers
By Applying the rule, m-5 x m-2 = m(-5)+(-2)
=m-5-2 =m-7
Same base(m)
By applying the rules of integer, if numbers having same sign, add the numbers and put that sign
By Applying the rule,
am ÷ an = am-n
Subtracting the powers
By Applying the rule, m-5 ÷ m-2 = m-5-(-2) =
m-5+2 = m-3
Same base(m)
By applying the rules of integer, if numbers having different sign, subtract the numbers and put the bigger number sign

5. Subtracting the powers
Examples for fractions:
By Applying the rule,
am x bm = (a x b)m
Multiplying the base
By Applying the rule,
Same powers(2)
By Applying the rule,
Dividing the base
By Applying the rule,
Same powers(2)
By Applying the rule,
By Applying the rule,
am x an = am+n
Adding the powers
Same base
By Applying the rule,
am ÷ an = am-n
Subtracting the powers
By Applying the rule,
Same base

6. Example for not applying the rule
Bases and powers are different
We cannot apply any rule
Bases and powers are different
We cannot apply any rule

7. Recap
37 x 34
(-8)5÷(-8)3
a(-6)x a(-8)
54÷64

8. Try these
37 x 47
(-8)5 x (-4)5
a6 ÷ t6
54 x 62