Indices Rules 1

Slide 1 : Multiplication Rule ya x yb = ya+b Why? 22 x 23 = 2 x 2 x 2 x 2 x 2 = 25 Examples: 67 x 64 = 67+4 = 611 54 x 5-2 = 54+(-2) = 52

Slide 2 : Division Rule ya / yb = ya-b Why? 25 / 23 = 2X2X2X2X2 / 2X2X2 = 2X2 = 22 Examples: 67 / 64 = 67-4 = 63 54 / 5-2 = 54-(-2) = 56

Slide 3 : Brackets 1 The position of the brackets are very important when calculating indices. Be careful with negatives -32 does not equal (-3)2 -32 = - 9 (-3)2 = 9

Slide 4 : Even powers of negative numbers allow for the negative values to be arranged in pairs. This pairing guarantees that the answer will always be positive. (-5)6 = (-5)•(-5) • (-5)•(-5) • (-5)•(-5) ? All pairs. = 25 • 25 • 25 = 15625 (a positive answer)? Odd powers of negative numbers, however, always leave one factor of the negative number not paired. This one lone negative term guarantees that the answer will always be negative. (-5)5 = (-5)•(-5) • (-5)•(-5) • (-5) ?One lone, un-paired, negative. = 25 • 25 • (-5)? = -3125 (a negative answer)?

Slide 5 : Brackets 2 (xm)n = xmn (xy)n = xnyn (x/y)n = xn/yn Examples: (x2)3 = x2×3 = x6 (xy)3 = x3y3 (x/y)2 = x2 / y2