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Mastering Exponents: Laws & Simplification Techniques

Learn to multiply monomials, simplify expressions, and apply laws of exponents effectively. Discover the power of combining numbers and variables seamlessly. Examples and practice included.

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Mastering Exponents: Laws & Simplification Techniques

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  1. 5.2 ExponentsObjectivesThe student will be able to: 1. Multiply monomials. 2. Simplify expressions with monomials. 3. Learn and apply the laws of exponents concerning powers of powers.

  2. A monomial is a 1. number, 2. variable, or 3. a product of one or more numbers and variables. Examples: 5 y 3x2y3

  3. Why are the following not monomials?x + y addition division 2 - 3a subtraction

  4. Law of Exponents am ∙ an = am+n

  5. Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 1) x2 • x4 x • x • x • x • x • x x2+4 x6

  6. Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 2) 2a2y3 • 3a3y4 6a5y7

  7. Simplify m3(m4)(m) • m7 • m8 • m12 • m13

  8. Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 1) x13 • x20 x33 2) 5a6y9 • 4a2y14 20a8y23

  9. Law of Exponents (am)n= amn

  10. Power of a Power When you have an exponent with an exponent, you multiply those exponents. 1) (x2)3 x2• 3 x6 2) (y3)4 y12

  11. Simplify (p2)4 1) p2 2) p4 3) p8 4) p6

  12. Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. (2a)3 23a3 8a3 (3x)2 9x2

  13. Simplify (4r)3 • 12r3 • 12r4 • 64r3 • 64r4

  14. Power of a Monomial 1) (x3y2)4 x3• 4 y2• 4 x12 y8 2) (4x4y3)3 64x12y9

  15. Power of a Monomial What about the order of operations? 3x(2x2)3 3x ∙ (23x6) 3x ∙ (8x6) =24x7

  16. Power of a Monomial What about the order of operations? 5r(3r3)4 5r ∙ (34r12) 5r ∙ (81r12) =405r13

  17. Simplify (3a2b3)4 • 12a8b12 • 81a6b7 • 81a16b81 • 81a8b12

  18. Assignment 5.2 Worksheet

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