1. LAWS OF EXPONENTS LAW 1: (base)power x (same base)another power
= (same base)add the powers
e.g. a3 x a5 = a3 + 5 = a8
e.g. (xy)2 x (xy)7 = (xy)2 + 7 = (xy)9

2. LAWS OF EXPONENTS LAW 2: (base)power ÷ (same base)another power
= (same base)subtract the second power from the first one
e.g. a7 ÷ a4 = a7 − 4 = a3
e.g. (xy)9 ÷ (xy)6 = (xy)9 − 6 = (xy)3

3. LAWS OF EXPONENTS LAW 3: ((base)power)another power
= (same base)multiply the powers
e.g. (a7)4 = a7 × 4 = a28
e.g. ((xy)9)6 = (xy)9 × 6 = (xy)54

4. LAWS OF EXPONENTS LAW 4(i): (base)power x (different base)same power
= (multiply the bases)same power
e.g. a7 x b7= (a x b)7 = (ab)7
e.g. (xy)9 x (pq)9 = (xy x pq)9 = (pqxy)9

5. LAWS OF EXPONENTS LAW 4(ii): (base)power ÷ (different base)same power
= (divide the bases)same power
e.g. a7 ÷ b7= (a ÷ b)7 = ( )7
e.g. (xy)9 ÷ (pq)9 = (xy ÷ pq)9 = ( )9

6. LAWS OF EXPONENTS DEFINITION 1: (non-zero base)0 = 1
e.g. a0 = e.g. 5a0 = 5 x a0 = 5 x (1) = 5
e.g. (xy)0 = e.g. -2(xy)0 = -2 x (1) = -2
e.g = e.g. 3(22)0 = 3 x (1) = 3

7. LAWS OF EXPONENTS DEFINITION 2: (non-zero base)-1 =
e.g. a-1 = e.g. 2a-1 = 2 x a-1 = 2 x =
e.g = e.g. 5(ab)-1 = 5 x (ab)-1 = 5 x =