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Exponent Laws #4 and #5

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These laws are generated (and understood) by extending an accepted numerical pattern… The second tier of the exponents laws takes us beyond the range of “common visualization”

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In general x 0 = 1 2 3 =8 2 2 =4 2 1 = 2 Continue the pattern 2 0 = 1 2 x 1 2 x 1 2 x 1

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This law holds true for any number! Any number to the exponent zero always reduces to 1 Continue the previous pattern..

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Is there a pattern? 2 -1 = 1 2121 2 -2 = 1 2 1 2 X= 2 -3 = 1 2 X 1 2 1 2 X = 12 1 2323

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In General X -n = 1 When given a negative exponent, invert the term and change the negative exponent to a positive exponent XnXn

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For example: 2 -3 = 1 2323 = 1 8 3 5 -2 = 5 3 2 5 3 = 5 3 X = 25 9

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3 -2 = 1 3232 = 1 9 (2x) 3 =8x 3 (x 4 )(x 3 ) =x7x7 (y 4 ) 5 =y 20 Try some others

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Warm-up ¼ + ¼ + ¼ = ½ + ½ = ¾ - ¼ = 2 5/13 + 7/13 =

Warm-up ¼ + ¼ + ¼ = ½ + ½ = ¾ - ¼ = 2 5/13 + 7/13 =

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