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INDICES

Exam Cog
①THE LAWS

ap × aq = ap+q

ap ÷ aq = ap−q

(ap)q = apq

⚠ Same base only.
②ZERO & NEGATIVE

a0 = 1

a−p = 1 / ap

e.g. 5−2 = 1/25

③BRACKETS

(ab)p = apbp

(a/b)p = ap/bp

(3x)2 = 9x2

④FRACTIONAL / SURDS

a½ = √a

9 / √3 = 32/3½ = 33/2

⑤METHOD
  1. Same base? Add/subtract powers
  2. Bracket? Power everything inside
  3. Negative? Flip to a fraction
  4. Different bases? Work each out
⑥WATCH-OUTS
⚠ ap + aq does NOT simplify — the laws are for × and ÷ only.