Exponents Law : Multiplication 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 4 : am X bm = (ab)m This law explains how to multiply different Bases having similar exponent i.e. am X bm = (ab)m This law of Exponents applies to all non-zero integers a & b, where m and n can be any whole number Study following example to prove and understand this law: Example: 22 X 32 Solution: This proceeds as: 22 X 32 Expand the given exponential forms and we get: = 2 X 2 X 3 X 3 Or we can also write it as: = 2 X 3 X 2 X 3 Now, observe carefully you can prepare two groups i.e.: = (2 X 3) X (2 X 3) And this can also be written into following exponential form: = (2 X 3)2 [because (2 X 3) is written twice] Hence, we get 22 X 32 = (2 X 3)2 And this explained Law of exponent i.e. am X bm = (ab)m Explaining with the help of algebraic numbers: Prove: a4 x b4 = (a x b)4 Solution: Given algebraic expression is: a4 x b4 = (a x b)2 Let's first solve the LHS: a4 x b4 Expand the given exponential forms and we get: = a x a x a x a x b x b x b x b Or we can also write it as: = a x b x a x b x a x b x a x b Now, observe carefully you can prepare groups as shown below: = (a x b) x (a x b) x (a x b) x (a x b) ..... (Statement 1) Now, solve the RHS: (a x b)4 Expand the given exponential form and we get: = (a x b) x (a x b) x (a x b) x (a x b) ..... (Statement 2) From Statement 1 and 2, we get: LHS = RHS Hence it's proved that: a4 x b4 = (a x b)4 And this explained Law of exponent i.e. am X bm = (ab)m Study More Solved Questions / Examples Simplify the below exponential form A) 53 X 54 57 B) 23 X 34 X 4 3 X 32