Exponents Law : Division of different Bases with Same Power

am X an = am+n	am ÷ an = am-n	( am )n = am n	am X bm = (ab)m	am ÷ bm = (a/b)m
a0 = 1	a-m

Exponent Law 5 : am ÷ bm = (a/b)m This law explains division of different Bases with Same Exponents am ÷ bm = (a/b)m This law of Exponents applies to all non-zero integers a & b, where m can be any whole number Study following example to prove and understand this law: Example: Solve 23 ÷ 33 Solution: This proceeds as: 23 ÷ 33 Expand the given exponential forms and we get: = (2 X 2 X 2) ÷ (3 X 3 X 3) Or we can also write it as: = 2 ÷ 3 X 2 ÷ 3 X 2 ÷ 3 Now, observe carefully you can prepare three groups i.e.: = (2 ÷ 3) X (2 ÷ 3) X (2 ÷ 3) And this can also be written into following exponential form: = (2 ÷ 3)3 [because ((2 ÷ 3) is written thrice] Hence, we get 23 ÷ 33 = (2 ÷ 3)3 And this explained Law of exponent i.e. am ÷ bm = (a/b)m Explaining with the help of algebraic numbers Prove: a5 ÷ b5 = (a ÷ b)5 Solution: Given algebraic expression is: a5 ÷ b5 = (a ÷ b)5 Let's first solve the LHS: a5 ÷ b5 Expand the given exponential forms and we get: = (a x a x a x a x a) ÷ (b x b x b x b x b) Or we can also write it as: = a ÷ b x a ÷ b x a ÷ b x a ÷ b x a ÷ b Now, observe carefully you can prepare groups as shown below: = (a ÷ b) x (a ÷ b) x (a ÷ b) x (a ÷ b) x (a ÷ b) ..... (Statement 1) Now, solve the RHS: (a ÷ b)5 Expand the given exponential form and we get: = (a ÷ b) x (a ÷ b) x (a ÷ b) x (a ÷ b) x (a ÷ b) ..... (Statement 2) From Statement 1 and 2, we get: LHS = RHS Hence it's proved that: a5 ÷ b5 = (a ÷ b)5 And this explained Law of exponent i.e. am ÷ bm = (a/b)m