Zero and Negative ExponentsPresentation Transcript
In the opening slide, we are using Adobe Photoshop to shrink down alarge digital camera photo to one quarter of its original size.We need to do this so that the photo can fit and load faster ontoFacebook, or any other website we put it on.Did you know that a computer cannot actually do Fractions or Percentsduring its processing?To figure out what one quarter equals, at a low level the computeractually uses NEGATIVE powers of 2, (associated with "Binary"processing that all computerised devices use).If it wasnt for Negative Exponents, we would not have all of thewonderful photo processing apps that are currently available.
We have two correct answers, but they are different toeach other. This means that the following must be true:232 x 2 x 2 8232 x 2 x 2 8== = 12323 = 23 – 320=201=
Any Value to the Power of Zero Equals 1 : a0= 1The Index Power of Zero, using patterns of Powersworks out like this:23= 2 x 2 x 2 = 822= 2 x 2 = 421= 2 = 220= 1Subtract 1from PowerSubtract 1from PowerSubtract 1from PowerDivide by 2Divide by 2Divide by 2
9999901=Any Value to the Power of Zero Equals 1 : a0= 1m01=3k03 x k03 x 1 3= = =50b250x b21 x b2b2= = =4a2b04 x a2x b04a2= =
We have two correct answers, but they are different toeach other. This means that the following must be true:222 x 2 1232 x 2 x 2 2==2223 = 22 – 32-1=2-1=12
Negative Exponents Produce Fractions : a-m= 1/aNegative Exponents, using patterns of Powersworks out like this:22= 2 x 2 = 421= 2 = 220= 12-1=Subtract 1from PowerSubtract 1from PowerSubtract 1from PowerDivide by 2Divide by 2Divide by 212
Note “a” cannot be zero, because 1/0 is not possible .A Negative exponent means we have tore-write our Power term as a 1/ Fraction.Negative Exponents are Positive Fractions.
Due to the way flipped over fractions called “Reciprocals” work:An item in the TOP with a Negative Index Power moves to theBOTTOM , where it becomes a POSITIVE Index Power.An item in the BOTTOM with a Negative Index Power moves tothe TOP, where it becomes a POSITIVE Index Power.5-2= 1/52= 1/25 but 1/5-2= 52/1 = 252-3545-423= 2222x 323-2 =4 x 9 = 36=
Simplify the expression (m3)-2x (m2)5We apply the Power Rule to both items:(m3)-2x (m2)5= m3 x -2x m2 x 5= m-6x m10= m10We now finish our taskby moving the NegativePower item into thebottom of a Fractionm6
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