Worksheet: Simplifying Monomials Using the Quotient Rule

In this worksheet, we will practice simplifying monomials using the quotient of powers.

Q1:

Simplify ๐‘ฅ ร— ๐‘ฅ ร— ๐‘ฅ ๐‘ฅ ร— ๐‘ฅ ร— ๐‘ฅ ๏Šฏ ๏Šซ ๏Šฌ ๏Šฌ ๏Šฎ ๏Šจ .

  • A 1 ๐‘ฅ ๏Šช
  • B ๐‘ฅ ๏Žฃ ๏Žค ๏Ž  ๏Žฅ
  • C ๐‘ฅ ๏Žค ๏Žฃ
  • D ๐‘ฅ ๏Šช

Q2:

Simplify ๐‘ฅ รท ๐‘ฅ 6 4 .

  • A ๐‘ฅ 2 4
  • B 2 ๐‘ฅ
  • C 2 ๐‘ฅ 2
  • D ๐‘ฅ 2

Q3:

Simplify ๏€น 6 ๐‘ฅ โˆ’ 3 ๐‘ฅ ๏… รท 3 ๐‘ฅ 3 3 2 .

  • A โˆ’ 6 ๐‘ฅ 4
  • B ๐‘ฅ 3
  • C ๐‘ฅ 4
  • D ๐‘ฅ
  • E โˆ’ 6 ๐‘ฅ

Q4:

Simplify ๐‘ฅ ร— ๐‘ฅ ๐‘ฅ ๏Šจ ๏Šฉ ๏Šฉ ๏Šซ ๏Šง ๏Šญ , where ๐‘ฅ โ‰  0 .

  • A ๐‘ฅ ๏Šง ๏Šง
  • B ๐‘ฅ ๏Šช ๏Šญ
  • C ๐‘ฅ ๏Šซ
  • D ๐‘ฅ ๏Šช ๏Šง

Q5:

Simplify ๐‘ฅ ๐‘ฆ ร— ๐‘ฅ ๐‘ฆ ๐‘ฅ ๐‘ฆ ๏Šช ๏Šช ๏Šจ ๏Šช ๏Šช ๏Šฉ .

  • A ( ๐‘ฅ ๐‘ฆ ) ๏Šญ
  • B ๐‘ฅ ๐‘ฆ ๏Šจ ๏Ž  ๏Žฅ ๏Žข
  • C ๐‘ฅ ๐‘ฆ ๏Šฌ ๏Šฉ
  • D ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šซ
  • E ( ๐‘ฅ ๐‘ฆ ) ๏Šง ๏Šจ

Q6:

Simplify 6 ร— 6 ร— 6 ร— 6 ร— 6 ร— 6 6 + 6 + 6 + 6 + 6 + 6 ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ ๏˜ .

  • A 6 ๏Šซ ๏˜
  • B 6 ๏Šซ ๏˜ ๏Šฐ ๏Šง
  • C 6 ๏Šฌ ๏˜ ๏Šฑ ๏Šง
  • D 6 ๏Šซ ๏˜ ๏Šฑ ๏Šง
  • E 6

Q7:

Simplify 1 2 5 ร— 2 5 2 5 ร— 5 ๏Š ๏Šฑ ๏Šง ๏Šฑ ๏Š ๏Š .

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

Q8:

Simplify 4 ร— 4 ( 4 ) ร— 1 6 ๏— ๏Šช ๏— ๏Šฉ ๏— ๏Šฑ ๏Šช ๏— .

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

Q9:

Simplify ๐‘Ž + ๐‘Ž + ๐‘Ž ๐‘Ž + ๐‘Ž + ๐‘Ž ๏— ๏Šฐ ๏Šฏ ๏— ๏Šฐ ๏Šฎ ๏— ๏Šฐ ๏Šญ ๏— ๏Šฑ ๏Šจ ๏— ๏Šฑ ๏Šฉ ๏— ๏Šฑ ๏Šช .

  • A ๐‘Ž ๐‘ฅ
  • B ๐‘Ž ๏Šฉ
  • C1
  • D ๐‘Ž ๏Šง ๏Šง
  • E ๐‘Ž ๏Šฎ

Q10:

Calculate 7 ร— 5 โˆ’ 9 ร— 5 3 ร— 5 โˆ’ 5 ๏Šซ ๏Š ๏Šซ ๏Š ๏Šฐ ๏Šจ ๏Šซ ๏Š ๏Šฐ ๏Šง ๏Šซ ๏Š , giving your answer in its simplest form.

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

Q11:

Simplify 2 ร— 3 6 ๏Šจ ๏— ๏Šฐ ๏Šง ๏Šง ๏Šฐ ๏Šฉ ๏— ๏Šจ ๏— and evaluate this expression when ๐‘ฅ = 2 .

  • A 2 ร— 3 ๏Šช ๏— ๏Šฐ ๏Šง , 12
  • B 2 ร— 3 ๏— , 12
  • C 2 ร— 3 ๏Šช ๏— ๏Šฑ ๏Šง , 54
  • D 2 ร— 3 ๏Šง ๏Šฐ ๏— , 54
  • E 2 ร— 3 ๏Šง ๏Šฑ ๏— , 54

Q12:

Simplify 6 ร— 9 5 4 ๏Š ๏Š ๏Šฐ ๏Š ๏Ž  ๏Žก .

Q13:

What is the value of 2 ร— 4 8 ๏Šญ ๏Š ๏Šฐ ๏Šจ ๏Šญ ๏Š ๏Šฐ ๏Šฉ ๏Šญ ๏Š ?

Q14:

Simplify ๐‘ฅ รท ๐‘ฅ ๏Šจ , given that ๐‘ฅ โ‰  0 .

  • A ๐‘ฅ ๏Šจ
  • B ๐‘ฅ ๏Šฉ
  • C ๐‘ฅ ๏Ž  ๏Žก
  • D ๐‘ฅ ๏Šฑ ๏Šง
  • E โˆ’ ๐‘ฅ

Q15:

Which of the following is equal to ๐‘ฅ + 1 ๐‘ฅ ๏Šฉ ๏Šฉ , where ๐‘ฅ โ‰  0 ?

  • A ๐‘ฅ โˆ’ ๐‘ฅ ๏Šฉ ๏Šฑ ๏Šฉ
  • B 1 + ๐‘ฅ ๏Šฉ
  • C ๐‘ฅ + ๐‘ฅ ๏Šฉ ๏Šฑ ๏Šฉ
  • D 1 + ๐‘ฅ ๏Šฑ ๏Šฉ
  • E 1 + ๐‘ฅ

Q16:

Simplify 2 5 6 ร— 1 6 6 4 ร— 6 4 ๏— ๏Šฑ ๏— ๏Šฐ ๏— ๏Šฑ ๏Šง ๏— ๏Šฐ ๏Šจ ๏Ž  ๏Žฃ ๏Ž  ๏Žฃ .

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

Q17:

Simplify 1 5 ร— 2 7 3 ร— 5 ๏Šจ ๏Š ๏Šฐ ๏Šจ ๏Šฑ ๏Š ๏Š ๏Šจ ๏Š ๏Šฐ ๏Šจ , and evaluate this expression when ๐‘› = 2 .

  • A 3 ๏Šจ , 9
  • B 3 ๏Šฑ ๏Š ๏Šฐ ๏Šจ , 1
  • C 3 ๏Šฑ ๏Šจ ๏Š , 1 8 1
  • D 3 ๏Šฑ ๏Šจ ๏Š ๏Šฐ ๏Šจ , 1 9

Q18:

Simplify 4 4 1 7 9 .

  • A 4 1 0
  • B 4 7
  • C 4 2 6
  • D 4 8
  • E 4 2 5

Q19:

Simplify ๐‘ฅ ๐‘ฅ 3 6 .

  • A ๐‘ฅ 9
  • B ๐‘ฅ 3
  • C ๐‘ฅ โˆ’ 9
  • D ๐‘ฅ โˆ’ 3
  • E ๐‘ฅ โˆ’ 2

Q20:

Simplify ๐‘ฅ ๐‘ฅ 7 6 .

  • A ๐‘ฅ 2
  • B ๐‘ฅ 1 3
  • C 1 ๐‘ฅ
  • D ๐‘ฅ
  • E ๐‘ฅ 3

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