ZERO POWERS LESSON 17

X0 is defined to be equal to 1 ZERO EXPONENT X0 is defined to be equal to 1 X0 = 1, where x  0 Exponent Law #4 Any non zero base raised to the exponent zero equals 1

EXAMPLES 30 = 1 (42  43)0 = 1 37 32 ( ) = 1

1 , ( x  0) That is x-n = xn NEGATIVE EXPONENTS x-n is defined to be the reciprocal of xn 1 xn , ( x  0) That is x-n = Exponent Law #5

WHY IS THIS TRUE? WATCH THIS PATTERN 103 = 1000 102 = 100 101 = 10 100 = 1 10-1 = 0.1 or 10-2 = 0.01 or Zero Exponent – Exponent Law #4 1 10 Negative Exponent – Exponent Law #5 1 100

EXAMPLES: ( ) ZERO EXPONENTS (-5)0 = 1 - 30 = -1 (20)3 = (1)0=1 (-3)0 = 1 2 5 ( ) = 1 - (3)0 = - (1) = -1 (-610)0 = 1

EXAMPLES 1 3 1 43 3-1 4-3 NEGATIVE EXPONENTS = Remember that a negative exponent does not mean a negative number but the reciprocal number. 4-3 = 1 43

EXAMPLE Long Version Short Version = 4-5 4-3  4-5 4-3 = 43 45 = 1 42 = 1 45  43 Flip Reciprocal to make positive powers Subtract powers and place where there are more. 1 45 43 =  = 1 42 43 45 = = 4-2

EXAMPLE Long Version Short Version = 33 3-5  33 3-5 = 3335 1 = 38 = 33 1  35 Flip Reciprocal to make positive powers Add powers and place where there are more. 33 1 35 =  = 38 = 33 35 

EXAMPLE Long Version Short Version = 5-2 54  5-2 54 = 1 (52)(54) = 1 56 = 1 52  54 Flip Reciprocal to make positive powers Add powers and place where there are more. 1 52 54 =  = 1 56 = 1 5254

CLASSWORK Zero and Negative Power Handout – Lesson 17