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Product and Quotient Rules: Classroom Packet

Grade 8 Algebra: Product and Quotient Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Same base, no coefficients

  1. 1. Simplify:
    23⋅242^3 \cdot 2^4
  2. 2. Simplify:
    x2⋅x5x^2 \cdot x^5
  3. 3. Simplify:
    a⋅a3a \cdot a^3
  4. 4. Simplify:
    5652\dfrac{5^6}{5^2}
  5. 5. Simplify:
    y9y3\dfrac{y^9}{y^3}
  6. 6. Simplify:
    m4⋅m4m^4 \cdot m^4

Answer Key

Level 1

  1. 1. 272^7
  2. 2. x7x^7
  3. 3. a4a^4
  4. 4. 545^4
  5. 5. y6y^6
  6. 6. m8m^8

Grade 8 Algebra: Product and Quotient Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 2

With coefficients

  1. 1. Simplify:
    3x2⋅4x33x^2 \cdot 4x^3
  2. 2. Simplify:
    (−2a4)(5a)(-2a^4)(5a)
  3. 3. Simplify:
    12y73y2\dfrac{12y^7}{3y^2}
  4. 4. Simplify:
    20m85m3\dfrac{20m^8}{5m^3}
  5. 5. Simplify:
    2x2y⋅3xy42x^2y \cdot 3xy^4
  6. 6. Simplify:
    18a5b36a2b\dfrac{18a^5b^3}{6a^2b}

Answer Key

Level 2

  1. 1. 12x512x^5
  2. 2. −10a5-10a^5
  3. 3. 4y54y^5
  4. 4. 4m54m^5
  5. 5. 6x3y56x^3y^5
  6. 6. 3a3b23a^3b^2

Grade 8 Algebra: Product and Quotient Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Several factors

  1. 1. Simplify:
    x3⋅x4⋅x2x^3 \cdot x^4 \cdot x^2
  2. 2. Simplify:
    (2a3)(3a2)(a)(2a^3)(3a^2)(a)
  3. 3. Simplify:
    4x5⋅3x26x3\dfrac{4x^5 \cdot 3x^2}{6x^3}
  4. 4. Simplify:
    35⋅3234\dfrac{3^5 \cdot 3^2}{3^4}
  5. 5. Simplify:
    (−3x2y)(2xy3)6x2y2\dfrac{(-3x^2y)(2xy^3)}{6x^2y^2}
  6. 6. Simplify:
    10m6n42m2n\dfrac{10m^6n^4}{2m^2n}

Answer Key

Level 3

  1. 1. x9x^9
  2. 2. 6a66a^6
  3. 3. 2x42x^4
  4. 4. 333^3
  5. 5. −xy2-xy^2
  6. 6. 5m4n35m^4n^3