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Multiplication, ADD the Indices: x12 × x4 = x x7 × x2 = x x5 × x3 = x am × an = am+n Multiplication, ADD the Indices: Multiply the numbers, add the indices. 3y10 × 2y8 = y 10x5 × 3x4 = x 5a3 × 2a4 = 10a7 Multiplication, ADD the Indices: 2xy3 × 4x3y3 = x y x2y2 × x3y5 = x y Put all those skills together.... Division, SUBTRACT the Indices: c10 ÷ c4 = c x5 ÷ x3 = x y8 ÷ y6 = y am ÷ an = am−n Division, SUBTRACT the Indices: Divide the numbers, subtract the indices. 10y10 ÷ 2y8 = y 30x7 ÷ 10x2 = x 6a5 ÷ 2a3 = 3a2 Division, SUBTRACT the Indices: Put all those skills together.... 15x4y11 ÷ 5xy7 = x y x8y4 ÷ x3y2 = x y Power of powers, MULTIPLY the indices. (g2)10 = g (x5)3 = x (a1)7 = a (am)n = am×n Power of powers, MULTIPLY the indices. Raise the number to the power, multiply the indices. (Calculator: 43) (4y10)3 = y (2x4)5 = x (3a2)4 = 81a8 , Calculator: 34 = 81 Power of powers, MULTIPLY the indices. Put all those skills together.... (x4y2)2 = x y (2y2z4)3 = y z , 7b0 = Only the values the indices are attached to, become one. 2y0 = The Zero Index: x0 = BUT... w0 = (7b)0 = 5a0 = 5 a0 = 1 (4a)0 + 2b0 = 5x0 − 2 = = 4 × 1 + 4 = 8 4x0 + 4 e−5 = Negative Indices: 1 e a−n = a−2 = an 1 1 a Write as a basic fraction: Negative Indices: 5−2 = 1 10−4 = 2−3 = Calculator: 23 = 8 23 1 = 1 8 1 |