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All Power Rules


Here are all the power rules compiled into one place for reference.

Rule

Power Rules

an am = an+m an am = anm (ab) c = abc (a b)n = an bn (a b)n = an bn a = a1 2 (an)m = amn = amn (a bn)m = amn bmn = am n bm n an = 1 an a0 = 1 a1 = a

an am = an+m an am = anm (ab) c = abc (a b)n = an bn (a b)n = an bn a = a1 2 (an)m = amn = amn (a bn)m = amn bmn = amn bmn an = 1 an a0 = 1 a1 = a

Remember that (a + b)nan + bn. This identity is valid only for multiplication and division, not addition and subtraction.

Example 1

Simplify (2a)3 (a b)2

You use the rules above and get (2a)3 = 23 a3 and (a b)2 = a2 b2. This gives you

= 23 a3 a2 b2 = 8 a3 a2 b2 = 8 a3+2 b2 = 8a5b2

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