Extended Number Lecture 5 abbreviated 2016b.pdf

# Extended Number Lecture 5 abbreviated 2016b.pdf - Laws of...

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Laws of Index notation In addition to knowing… How to raise positive bases to a positive power That any number raised to the power of 1 is itself That any number raised to the power of zero is 1 How to raise bases to a negative power How to raise negative bases to a power How to raise bases to a fractional power How to raise factorised bases to a power How to raise fractional bases to a power You will also learn the laws of exponents

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Laws of Exponents Product Rule Quotient Rule Power Rule
Product Rule For any nonzero real number X, and for any non negative integers a and b….. X a . X b = X a+b e.g. 5 3 x 5 4 = 5 (3+4) = 5 7 4 2 x 4 3 = 4 5 3 7 x 3 2 = 3 9 10 5 x 10 12 = 10 17 10 3 x 5 4 = ……. 10 3 x 5 4

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Quotient Rule Very similar (and derivable) 4 5 /4 3 = 4 2 5 3 /5 4 = 5 -1 = 1/5 6 3 /6 -2 = 6 (3-(-2)) = 6 5 X b X a = X (a-b)
Sneakiness (combining rules) What about 16 5 x 4 3 ?

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