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7-1: Multiplication Properties of Exponents

7-1: Multiplication Properties of Exponents. 7-1: Multiplication Properties of Exponents. Monomial : A number, variable, or the product of a number and one or more variables Constant : A monomial that is a real number Example 1: Identifying monomials

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7-1: Multiplication Properties of Exponents

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  1. 7-1: Multiplication Properties of Exponents

  2. 7-1: Multiplication Properties of Exponents • Monomial: A number, variable, or the product of a number and one or more variables • Constant: A monomial that is a real number • Example 1: Identifying monomials • Determine whether each expression is a monomial. Explain. • 10 • Yes; it’s a constant, so it’s a monomial • f + 24 • No; the expression has addition, so it has more than one term • h2 • Yes; it’s the product of variables • j • Yes; single variables are monomials

  3. 7-1: Multiplication Properties of Exponents • Your Turn • Determine whether each expression is a monomial. Explain. • -x + 5 • No; the expression has more than one term • 23abcd2 • Yes; product of number and variables • Yes; product of number and variables

  4. 7-1: Multiplication Properties of Exponents • Product of Powers • To multiply two powers that have the same base, add their exponents • Examples • b3● b5 = b3+5 = b8 • g4● g6 = g4+6 = g10

  5. 7-1: Multiplication Properties of Exponents • Example 2: Simplify each expression • (6n3)(2n7) • (6n3)(2n7) = (6 ● 2)(n3● n7) • = (6 ● 2)(n3+7) • = 12n10 • (3pt3)(p3t4) • (3pt3)(p3t4) = (3 ● 1)(p ● p3)(t3● t4) • = (3 ● 1)(p1+3)(t3+4) • = 3p4t7

  6. 1) Simplify (5x2)(4x3) • 9x5 • 20x5 • 20x6 • 9x6

  7. 2) Simplify 3xy2(-2x2y3) • 6xy5 • -6x2x6 • 1x3y5 • -6x3y5

  8. 7-1: Multiplication Properties of Exponents • Power to a power • When an exponent is on the outside of parenthesis, multiply exponents • Examples • (b3)5 = b3●5 = b15 • (g6)7 = g6●7 = g42

  9. 7-1: Multiplication Properties of Exponents • Example 3: Simplify each expression • [(23)2]4 • [(23)2]4 = 23●2●4 • = 224 • (-2f2g3h2)3 • (-2f2g3h2)3 = (-2)3(f2)3(g3)3(h2)3 • = (-2)3(f2●3)(g3●3)(h2●3) • = -8f6g9h6

  10. 3) Simplify [(42)2]3 • 47 • 48 • 412 • 410

  11. 4) Simplify (5k2)3 • 125k6 • 125k5 • 5k6 • 5k8

  12. Leader Board

  13. 7-1: Multiplication Properties of Exponents • Assignment • Page 394 – 395 • 1 – 15 & 21 – 37 (odds)

  14. 7-1: Multiplication Properties of Exponents Day 2

  15. 7-1: Multiplication Properties of Exponents • To simplify a monomial expression • Simplify any power to a power • Simplify any product of powers • Example 3: Simplify (3xy4)2[(-2y)2]3 • (3xy4)2[(-2y)2]3 Power to power • (3xy4)2(-2y)6Power to power • 32x2y8(-2)6y6Simplify numers • 9x2y8(64)y6Product of powers • 576x2y14

  16. 5) Simplify (4x2y)(2xy2z3)3 • 8x5y7z9 • 32x6y6z9 • 32x5y7z9 • 24x5y7z9

  17. 6) Simplify [(2c2d3)2]3(3c5d2)3 • 1728c27d24 • 6c7d5 • 24c13d10 • 5c7d21

  18. Leader Board

  19. 7-1: Multiplication Properties of Exponents • Assignment • Page 394 – 395 • 17 – 19 & 41 – 55 (odds)

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