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7-2: Division Properties of Exponents

Learn how to simplify fractions using repeated multiplication, divide powers with the same base, utilize zero exponent and negative exponent properties, and complete exercises for practice.

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7-2: Division Properties of Exponents

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  1. 7-2: Division Properties of Exponents

  2. 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.

  3. 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

  4. 7-2: Division Properties of Exponents • Example 1: Simplify. Assume that x and y are not equal to zero

  5. 1) Simplify • a4b11 • a2b7

  6. 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

  7. 7-2: Division Properties of Exponents • Example 2: Simplify. Assume that x and y are not equal to zero

  8. 2) Simplify

  9. 7-2: Division Properties of Exponents • Assignment • Page 402-403 • 1 – 11 & 19 – 29 • Odd problems only

  10. 7-2: Division Properties of Exponents Day 2

  11. 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

  12. 7-2: Division Properties of Exponents • Example 3: Simplify. Assume that m and n are not equal to zero

  13. 3) Simplify • 3/5 • 1 • 0 • -1

  14. 4) Simplify • xk2 • (xk)2 • k2

  15. 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 =

  16. 7-2: Division Properties of Exponents • Example 4: Simplify. Assume no denominator is zero

  17. 5) Simplify

  18. 6) Simplify

  19. 7-2: Division Properties of Exponents • Assignment • Page 402-403 • 13 – 17 • 31 – 41 • 45 - 55 • Odd problems only

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