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7-2: Division Properties of Exponents
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7-2: Division Properties of Exponents
You can use repeated multiplication to simplify fractions. Expand the numerator and denominator using repeated multiplication. Then cancel like terms.
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7-2: Division Properties of Exponents
Note that 7 – 4 = 3, and 4 – 3 = 1 Quotient of Powers To divide two powers that have the same base, subtract the denominator exponent from the numerator exponent. Examples
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7-2: Division Properties of Exponents
Example 1: Simplify. Assume that x and y are not equal to zero
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1) Simplify a4b11 a2b7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
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7-2: Division Properties of Exponents
Power of a quotient Just like with multiplication, when an exponent is on the outside of parenthesis, multiply exponents Examples
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7-2: Division Properties of Exponents
Example 2: Simplify. Assume that x and y are not equal to zero
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2) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
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7-2: Division Properties of Exponents
Assignment Page 1 – 11 & 19 – 29 Odd problems only
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7-2: Division Properties of Exponents
Day 2
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7-2: Division Properties of Exponents
Zero Exponent Property Any nonzero number raised to a zero power is equal to 1 Examples 150 = 1 (b/c)0 = 1 (2/7)0 = 1
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7-2: Division Properties of Exponents
Example 3: Simplify. Assume that m and n are not equal to zero
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3) Simplify 3/5 1 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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4) Simplify xk2 (xk)2 k2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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7-2: Division Properties of Exponents
Negative Exponent Property Negative exponents mean move the base to the other side of a fraction, and turn the exponent positive Examples 2-4 =
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7-2: Division Properties of Exponents
Example 4: Simplify. Assume no denominator is zero
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5) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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6) Simplify 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
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7-2: Division Properties of Exponents
Assignment Page 13 – 17 31 – 41 Odd problems only
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