Exponents Law : any non-zero integer having exponent as Zero is always equals to 1

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 6 : a0 = 1 Before you understand this topic, you are advice to read: Law of Exponent : am ÷ an = am-n This law explains that any non-zero integer having exponent as Zero is always equals to 1 Algebraic representing of this law is a0 = 1 Let proved this with the help of following example: Example: Solve a5 ÷ a5 Solution: Given exponential forms: a5 ÷ a5 Expand the given exponential form and we get = a x a x a x a x a ÷ a x a x a x a x a Solve the division expression and we get: = 1 Therefore we get: a5 ÷ a5 = 1 ..... (Statement 1) Now once again take the given exponential forms: a5 ÷ a5 Apply the law of exponential i.e. am ÷ an = am-n and we get: = a5 - 5 Solve the exponents and we get: = a0 Therefore we get: a5 ÷ a5 = a0 ..... (Statement 2) From Statement 1 and 2, we get: a0 = 1 Hence, this proves the law: a0 = 1 Study the following example to further understand this: Example: Solve 23 ÷ 23 Solution: Given exponential forms: 23 ÷ 23 Expand the given exponential form and we get = 2 X 2 X 2 ÷ 2 X 2 X 2 Solve the division expression and we get: = 1 Therefore we get: 23 ÷ 23 = 1 ..... (Statement 1) Now once again take the given exponential forms: 23 ÷ 23 Apply the law of exponential i.e. am ÷ an = am-n and we get: = 23 - 3 Solve the exponents and we get: = 20 Therefore we get: 23 ÷ 23 = 20 ..... (Statement 2) From Statement 1 and 2, we get: 20 = 1 Hence, this proves the law: a0 = 1