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Worksheet: Simplifying Monomials with Quotient of Powers

Q1:

Simplify π‘₯ Γ— π‘₯ π‘₯ 2 3 3 5 1 7 , where π‘₯ β‰  0 .

  • A π‘₯ 1 1
  • B π‘₯ 4 7
  • C π‘₯ 5
  • D π‘₯ 4 1

Q2:

Simplify π‘₯ Γ— π‘₯ π‘₯ 2 5 2 1 1 6 , where π‘₯ β‰  0 .

  • A π‘₯ 1 9
  • B π‘₯ 3 2
  • C π‘₯ 2 0
  • D π‘₯ 3 0

Q3:

Simplify π‘₯ Γ— π‘₯ Γ— π‘₯ π‘₯ Γ— π‘₯ Γ— π‘₯ 9 5 6 6 8 2 .

  • A 1 π‘₯ 4
  • B π‘₯ 4 5 1 6
  • C π‘₯ 5 4
  • D π‘₯ 4

Q4:

Simplify π‘₯ 𝑦 Γ— π‘₯ 𝑦 π‘₯ 𝑦 4 4 2 4 4 3 .

  • A ( π‘₯ 𝑦 ) 7
  • B π‘₯ 𝑦 2 1 6 3
  • C π‘₯ 𝑦 6 3
  • D π‘₯ 𝑦 2 5
  • E ( π‘₯ 𝑦 ) 1 2

Q5:

Simplify π‘₯ 𝑦 Γ— π‘₯ 𝑦 π‘₯ 𝑦 2 4 5 4 6 2 .

  • A ( π‘₯ 𝑦 ) 7
  • B π‘₯ 𝑦 5 3 8
  • C π‘₯ 𝑦 3 2
  • D π‘₯ 𝑦 6
  • E ( π‘₯ 𝑦 ) 1 6

Q6:

Simplify π‘₯ 𝑦 Γ— π‘₯ 𝑦 π‘₯ 𝑦 4 6 3 4 7 5 .

  • A ( π‘₯ 𝑦 ) 5
  • B π‘₯ 𝑦 1 2 7 2 4 5
  • C π‘₯ 𝑦 8 7
  • D 𝑦 5
  • E π‘₯ 𝑦

Q7:

Simplify 6 Γ— 6 Γ— 6 Γ— 6 Γ— 6 Γ— 6 6 + 6 + 6 + 6 + 6 + 6 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 𝑦 .

  • A 6 5 𝑦
  • B 6 5 𝑦 + 1
  • C 6 6 𝑦 βˆ’ 1
  • D 6 5 𝑦 βˆ’ 1
  • E 6

Q8:

Simplify 1 2 5 Γ— 2 5 2 5 Γ— 5 𝑛 βˆ’ 1 βˆ’ 𝑛 𝑛 .

  • A150
  • B 3 125
  • C 1 1 5 0
  • D 1 3 1 2 5

Q9:

Simplify 4 Γ— 4 ( 4 ) Γ— 1 6 π‘₯ 4 π‘₯ 3 π‘₯ βˆ’ 4 π‘₯ .

  • A20
  • B 1 2 5 6
  • C 1 2 0
  • D256
  • E4

Q10:

Simplify π‘Ž + π‘Ž + π‘Ž π‘Ž + π‘Ž + π‘Ž π‘₯ + 9 π‘₯ + 8 π‘₯ + 7 π‘₯ βˆ’ 2 π‘₯ βˆ’ 3 π‘₯ βˆ’ 4 .

  • A π‘Ž π‘₯
  • B π‘Ž 3
  • C1
  • D π‘Ž 1 1
  • E π‘Ž 8

Q11:

Calculate 7 Γ— 5 βˆ’ 9 Γ— 5 3 Γ— 5 βˆ’ 5 5 𝑛 5 𝑛 + 2 5 𝑛 + 1 5 𝑛 , giving your answer in its simplest form.

  • A 5 1 4
  • B βˆ’ 2 1 8 3
  • C 5 3
  • D βˆ’ 1 0 9 7
  • E5

Q12:

Simplify 2 Γ— 3 6 2 π‘₯ + 1 1 + 3 π‘₯ 2 π‘₯ and evaluate this expression when π‘₯ = 2 .

  • A 2 Γ— 3 4 π‘₯ + 1 , 12
  • B 2 Γ— 3 π‘₯ , 12
  • C 2 Γ— 3 4 π‘₯ βˆ’ 1 , 54
  • D 2 Γ— 3 1 + π‘₯ , 54
  • E 2 Γ— 3 1 βˆ’ π‘₯ , 54

Q13:

Simplify 6 Γ— 9 5 4 𝑛 𝑛 + 𝑛 1 2 .

Q14:

What is the value of 2 Γ— 4 8 7 𝑛 + 2 7 𝑛 + 3 7 𝑛 ?

Q15:

Simplify π‘₯ Γ· π‘₯ 2 , given that π‘₯ β‰  0 .

  • A π‘₯ 2
  • B π‘₯ 3
  • C π‘₯ 1 2
  • D π‘₯ βˆ’ 1
  • E βˆ’ π‘₯

Q16:

Which of the following is equal to π‘₯ + 1 π‘₯ 3 3 , where π‘₯ β‰  0 ?

  • A π‘₯ βˆ’ π‘₯ 3 βˆ’ 3
  • B 1 + π‘₯ 3
  • C π‘₯ + π‘₯ 3 βˆ’ 3
  • D 1 + π‘₯ βˆ’ 3
  • E 1 + π‘₯

Q17:

Simplify 2 5 6 Γ— 1 6 6 4 Γ— 6 4 π‘₯ βˆ’ π‘₯ + π‘₯ βˆ’ 1 π‘₯ + 2 1 4 1 4 .

  • A 1 8
  • B 1 2
  • C 1 2 0 4 8
  • D 1 1 2 8

Q18:

Simplify 1 5 Γ— 2 7 3 Γ— 5 2 𝑛 + 2 βˆ’ 𝑛 𝑛 2 𝑛 + 2 , and evaluate this expression when 𝑛 = 2 .

  • A 3 2 , 9
  • B 3 βˆ’ 𝑛 + 2 , 1
  • C 3 βˆ’ 2 𝑛 , 1 8 1
  • D 3 βˆ’ 2 𝑛 + 2 , 1 9