Worksheet: Simplifying Monomials: Power of a Power Rule

In this worksheet, we will practice simplifying algebraic expressions as monomials involving single and multiple variables using the power of a power property.

Q1:

Which of the following is equal to 3?

  • A3
  • B3
  • C3
  • D3
  • E3

Q2:

Simplify (𝑥).

  • A𝑥
  • B𝑥
  • C𝑥
  • D𝑥

Q3:

Simplify 𝑥𝑦.

  • A𝑥𝑦
  • B𝑥𝑦
  • C𝑥𝑦
  • D𝑥𝑦

Q4:

What is the value of 6+6?

Q5:

Is it true that 𝑎=𝑎?

  • AYes
  • BNo

Q6:

Which of the following is equal to 4?

  • A4
  • B4
  • C4
  • D4

Q7:

Write an equivalent expression to 𝑥𝑦𝑧 that does not include brackets.

  • A𝑥𝑦𝑧
  • B𝑥𝑦𝑧
  • C𝑥𝑦𝑧
  • D𝑥𝑦𝑧
  • E3𝑥𝑦𝑧

Q8:

Simplify 𝑎𝑏𝑐𝑑.

  • A3𝑎𝑏𝑐𝑑
  • B𝑎𝑏𝑐𝑑
  • C𝑎𝑏𝑐𝑑
  • D𝑎𝑏3𝑐𝑑

Q9:

Simplify (𝑎÷𝑏).

  • A𝑎𝑏
  • B𝑎𝑏
  • C𝑎𝑏
  • D𝑎𝑏

Q10:

Simplify 𝑥𝑦.

  • A𝑥𝑦
  • B𝑥𝑦
  • C4𝑥𝑦
  • D𝑥4𝑦

Q11:

Simplify 𝑥𝑦𝑧.

  • A3𝑥𝑦𝑧
  • B𝑥𝑦3𝑧
  • C𝑥𝑦𝑧
  • D𝑥𝑦𝑧

Q12:

Simplify 𝑥.

  • A𝑥
  • B2𝑥
  • C12𝑥
  • D12𝑥
  • E𝑥

Q13:

What is the volume of a cube of edge length 5𝑥𝑦?

  • A15𝑥𝑦
  • B125𝑥𝑦
  • C25𝑥𝑦
  • D125𝑥𝑦

Q14:

Write expressions for the area and perimeter of a square of side length 4𝑥 cm.

  • Aarea =4𝑥cm, perimeter =16𝑥cm
  • Barea =16𝑥cm, perimeter =16𝑥cm
  • Carea =16𝑥cm, perimeter =16𝑥cm
  • Darea =16𝑥cm, perimeter =8𝑥cm

Q15:

Write a monomial that is equal to the area of this square.

  • A9𝑎𝑏
  • B9𝑎𝑏
  • C3𝑎𝑏
  • D6𝑎𝑏
  • E9𝑎𝑏

Q16:

Express the area of a square with sides of length 8𝑎𝑏 as a monomial.

  • A16𝑎𝑏
  • B8𝑎𝑏
  • C64𝑎𝑏
  • D8𝑎𝑏
  • E64𝑎𝑏

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