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

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

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

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

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

LAWS OF EXPONENTS DEFINITION 1: (non-zero base)0 = 1 e.g. a0 = 1 e.g. 5a0 = 5 x a0 = 5 x (1) = 5 e.g. (xy)0 = 1 e.g. -2(xy)0 = -2 x (1) = -2 e.g. 220 = 1 e.g. 3(22)0 = 3 x (1) = 3

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. 5-1 = e.g. 5(ab)-1 = 5 x (ab)-1 = 5 x =