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Power Rules: Classroom Packet

Grade 8 Algebra: Power Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Power of a power and of a product

  1. 1. Simplify:
    (x2)3(x^2)^3
  2. 2. Simplify:
    (23)2(2^3)^2
  3. 3. Simplify:
    (a4)5(a^4)^5
  4. 4. Simplify:
    (xy)3(xy)^3
  5. 5. Simplify:
    (3m)2(3m)^2
  6. 6. Simplify:
    (xy)4\left(\dfrac{x}{y}\right)^4

Answer Key

Level 1

  1. 1. x6x^6
  2. 2. 262^6
  3. 3. a20a^{20}
  4. 4. x3y3x^3y^3
  5. 5. 9m29m^2
  6. 6. x4y4\dfrac{x^4}{y^4}

Grade 8 Algebra: Power Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Coefficients and negatives

  1. 1. Simplify:
    (2x3)2(2x^3)^2
  2. 2. Simplify:
    (−3a2)3(-3a^2)^3
  3. 3. Simplify:
    (x2y3)4(x^2y^3)^4
  4. 4. Simplify:
    (5m4n)2(5m^4n)^2
  5. 5. Simplify:
    (2ab2)3\left(\dfrac{2a}{b^2}\right)^3
  6. 6. Simplify:
    (−x3)4(-x^3)^4

Answer Key

Level 2

  1. 1. 4x64x^6
  2. 2. −27a6-27a^6
  3. 3. x8y12x^8y^{12}
  4. 4. 25m8n225m^8n^2
  5. 5. 8a3b6\dfrac{8a^3}{b^6}
  6. 6. x12x^{12}

Grade 8 Algebra: Power Rules

Name: ______________________Date: ____________Score: ____ / 6

Level 3

Combine the rules

  1. 1. Simplify:
    (2x2)3⋅x(2x^2)^3 \cdot x
  2. 2. Simplify:
    (a2b)3(ab2)2(a^2b)^3(ab^2)^2
  3. 3. Simplify:
    (3x4)29x5\dfrac{(3x^4)^2}{9x^5}
  4. 4. Simplify:
    (2m3n)2(3mn2)(2m^3n)^2(3mn^2)
  5. 5. Simplify:
    (x3)2⋅x4x5\dfrac{(x^3)^2 \cdot x^4}{x^5}
  6. 6. Simplify:
    (−2y2)3(y3)2(-2y^2)^3(y^3)^2

Answer Key

Level 3

  1. 1. 8x78x^7
  2. 2. a8b7a^8b^7
  3. 3. x3x^3
  4. 4. 12m7n412m^7n^4
  5. 5. x5x^5
  6. 6. −8y12-8y^{12}