4.1: Prelude to Exponential and Logarithmic Functions including Exponential properties
Adding Exponents
a n * a m = a n+m
Example: a 2 * a 4 = a 2+4 = a 6
Subtracting Exponents
a n /a m = a n-m provided a not equal to 0
a 6 /a 2 = a 6 - 2 = a 4
Multiplying Exponents
(a n ) m = a n*m
Zero Exponent
a 0 = 1
Negative Exponents
a -n = 1/a n
1 in Exponent
a = a 1
Distributing Exponents
(ab) n = (a 1 b 1 ) n = a 1*n b 1*n = a n b n
(a/b) n = (a 1 / b 1 ) n = a 1*n / b 1*n = a n /b n
w 3 w 5 = ?
- Answer
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w 3+5 = w 8
y 6 /y 2 = ?
- Answer
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y 6-2 = y 4
(z 3 ) 5 = ?
- Answer
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z 3*5 = z 15
2345 0 = ?
- Answer
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Any number raised to the 0 power is 1.
t -6 = ?
- Answer
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t -6 = 1/t 6
4 1 = ?
- Answer
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4
(a 3 b 2 )4 = ?
- Answer
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a 3* 4 b 2 *4 = a 12 b 8