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Worksheet: Simplifying Exponential Expressions

Q1:

Write 7 β‹… 7 β‹… 7 β‹… 7 β‹… π‘Ž β‹… π‘Ž β‹… 2 β‹… 2 β‹… 2 β‹… 2 β‹… 2 β‹… 𝑏 β‹… 𝑏 β‹… 𝑏 using exponents.

  • A 7 β‹… π‘Ž β‹… 2 β‹… 𝑏 2 4 3 5
  • B 7 β‹… π‘Ž β‹… 2 β‹… 𝑏 βˆ’ 4 βˆ’ 2 βˆ’ 5 βˆ’ 3
  • C 7 β‹… π‘Ž β‹… 2 β‹… 𝑏 5 3 4 2
  • D 7 β‹… π‘Ž β‹… 2 β‹… 𝑏 4 2 5 3
  • E 7 β‹… π‘Ž β‹… 2 β‹… 𝑏 βˆ’ 5 βˆ’ 3 βˆ’ 4 βˆ’ 2

Q2:

Write 8 β‹… 8 β‹… 8 β‹… π‘Ž β‹… π‘Ž β‹… π‘Ž β‹… 2 β‹… 2 β‹… 𝑏 β‹… 𝑏 β‹… 𝑏 β‹… 𝑏 using exponents.

  • A 8 β‹… π‘Ž β‹… 2 β‹… 𝑏 3 3 4 2
  • B 8 β‹… π‘Ž β‹… 2 β‹… 𝑏 βˆ’ 3 βˆ’ 3 βˆ’ 2 βˆ’ 4
  • C 8 β‹… π‘Ž β‹… 2 β‹… 𝑏 2 4 3 3
  • D 8 β‹… π‘Ž β‹… 2 β‹… 𝑏 3 3 2 4
  • E 8 β‹… π‘Ž β‹… 2 β‹… 𝑏 βˆ’ 2 βˆ’ 4 βˆ’ 3 βˆ’ 3

Q3:

Write 4 Γ— 9 Γ— 4 Γ— 9 2 5 3 4 in the form π‘Ž 𝑏 π‘š 𝑛 , where π‘Ž and 𝑏 are prime numbers.

  • A 4 Γ— 3 1 0 9
  • B 2 Γ— 3 5 9
  • C 2 Γ— 9 1 0 1 8
  • D 2 Γ— 3 1 0 1 8

Q4:

Which of the following is equal to ο€Ό βˆ’ 3 4  3 ?

  • A βˆ’ 9 1 2
  • B 2 7 6 4
  • C 6 4 2 7
  • D βˆ’ 2 7 6 4
  • E βˆ’ 6 4 2 7

Q5:

Which of the following is equal to ο€Ό βˆ’ 2 1 4  3 ?

  • A βˆ’ 6 3 4
  • B βˆ’ 8 1 6 4
  • C βˆ’ 2 3 1 2
  • D βˆ’ 1 1 2 5 6 4
  • E βˆ’ 2 7 1 2

Q6:

Which of the following is equal to ( βˆ’ 3 ) Γ— ( βˆ’ 3 ) 3 4 ?

  • A108
  • B 5 3 1 4 4 1
  • C 2 1 8 7
  • D βˆ’ 2 1 8 7
  • E 9 7

Q7:

Write 3 4 3 Γ— 3 Γ— 3 4 3 Γ— 3 2 3 4 4 in the form π‘Ž 𝑏 π‘š 𝑛 where π‘Ž and 𝑏 are prime numbers.

  • A 3 4 3 Γ— 3 1 8 7
  • B 7 Γ— 3 6 7
  • C 3 4 3 Γ— 3 7 6
  • D 7 Γ— 3 1 8 7

Q8:

Which of the following has the same value as ο€Ή 3  2 4 ?

  • A 3 1 6
  • B 3 6
  • C36
  • D 3 8
  • E 6 4

Q9:

Simplify ( 2 5 ) Γ— ( 8 ) ( 1 0 0 ) Γ— √ 1 0 0 3 2 5 3 3 2 π‘₯ π‘₯ βˆ’ π‘₯ .

  • A320
  • B 1 6 5
  • C 5 1 6
  • D 1 3 2 0

Q10:

Determine the simplest form of ( 1 6 ) Γ— 2 7 ( 1 4 4 ) Γ— √ 8 1 3 2 1 3 3 2 π‘₯ π‘₯ βˆ’ π‘₯ .

  • A3
  • B 1 3
  • C27
  • D 1 2 7

Q11:

Which of the following is equal to 2 + 2 1 2 1 1 ?

  • A 2 Γ— 2 1 1
  • B 2 2 2
  • C 2 2 3
  • D 3 Γ— 2 1 1
  • E 3 Γ— 2 1 2

Q12:

Is the following correct: 2 = 2 Γ— 4 4 ?

  • A no
  • B yes

Q13:

Simplify the expression  𝑑 𝑣 𝑑 𝑣  3 8 βˆ’ 5 4 2 3 1 2 βˆ’ 2 3 .

  • A 𝑑 𝑣 3 2 1 6
  • B 𝑑 𝑣 7 6 7 3 6
  • C 𝑑 𝑣 βˆ’ 7 3 6 βˆ’ 7 6
  • D 𝑑 𝑣 7 3 6 7 6
  • E 𝑑 𝑣 7 3 7 3

Q14:

Write 3 4 in expanded form.

  • A 3 Γ— 4
  • B 4 + 4 + 4
  • C 4 Γ— 4 Γ— 4
  • D 3 Γ— 3 Γ— 3 Γ— 3
  • E 3 + 3 + 3 + 3

Q15:

Simplify ( 3 6 ) Γ— 8 6 Γ— ( 1 2 ) Γ— ο€» √ 1 6  π‘₯ + π‘₯ + 1 π‘₯ βˆ’ 1 π‘₯ + 5 π‘₯ βˆ’ 1 1 2 .

  • A216
  • B 1 8 6 4
  • C864
  • D 1 2 1 6

Q16:

Calculate .

  • A
  • B
  • C
  • D

Q17:

Calculate 6 + 6 + 6 + 6 + 6 + 6 9 9 9 9 9 9 .

  • A 6 5 4
  • B 6 9
  • C 3 6 9
  • D 6 1 0

Q18:

What is 2 + 4 3 1 0 1 5 5 ?

  • A 4 4 6 5
  • B 6 1 5 5
  • C 4 3 1 0
  • D 2 3 1 1
  • E 4 1 5 7

Q19:

Which of the following is equal to 2 βˆ’ 2 2 2 1 0 2 2 0 9 ?

  • A 2 209
  • B2
  • C 2 210
  • D 2 2 2 0 9
  • E 2 2 2 0 8

Q20:

Write 7 Γ— 7 Γ— 7 Γ— 7 in exponential form.

  • A 4 7
  • B 7 Γ— 4
  • C 7 Γ— 7 Γ— 7 Γ— 7
  • D 7 4
  • E 4 Γ— 7 4

Q21:

What is the exponent in 6 1 4 ?

Q22:

Simplify the expression 𝑑 𝑣 𝑑 𝑣 βˆ’ 3 8 5 4 βˆ’ 2 3 βˆ’ 1 2 .

  • A 𝑑 𝑣 7 4 7 4
  • B 𝑑 𝑣 7 4 7 2 4
  • C 𝑑 𝑣 βˆ’ 7 2 7 βˆ’ 7 4
  • D 𝑑 𝑣 7 2 4 7 4
  • E 𝑑 𝑣 2 4 7 4 7