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Worksheet: Simplifying Exponential Expressions

In this worksheet, we will practice simplifying numerical and algebraic expressions using exponentials and knowing the notation used for exponential expressions.

Q1:

Write 7 × 7 × 7 × 7 in exponential form.

  • A 4 7
  • B 7 × 4
  • C 7 × 7 × 7 × 7
  • D 7 4
  • E 4 × 7 4

Q2:

Write 3 4 in expanded form.

  • A 3 × 4
  • B 4 + 4 + 4
  • C 4 × 4 × 4
  • D 3 × 3 × 3 × 3
  • E 3 + 3 + 3 + 3

Q3:

What is the exponent in 6 1 4 ?

Q4:

Calculate − 4 5 × − 4 5 3 2 .

  • A 1 6 2 5 5
  • B − 4 5 6
  • C − 4 2 5 5
  • D − 4 5 5
  • E − 4 5 5

Q5:

Write 7 ⋅ 7 ⋅ 7 ⋅ 7 ⋅ 𝑎 ⋅ 𝑎 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 𝑏 ⋅ 𝑏 ⋅ 𝑏 using exponents.

  • A 7 ⋅ 𝑎 ⋅ 2 ⋅ 𝑏 2 4 3 5
  • B 7 ⋅ 𝑎 ⋅ 2 ⋅ 𝑏 − 4 − 2 − 5 − 3
  • C 7 ⋅ 𝑎 ⋅ 2 ⋅ 𝑏 5 3 4 2
  • D 7 ⋅ 𝑎 ⋅ 2 ⋅ 𝑏 4 2 5 3
  • E 7 ⋅ 𝑎 ⋅ 2 ⋅ 𝑏 − 5 − 3 − 4 − 2

Q6:

Is the following correct: 2 = 2 × 4 4 ?

  • A no
  • B yes

Q7:

Write 4 × 9 × 4 × 9 2 5 3 4 in the form 𝑎 𝑏 𝑚 𝑛 , where 𝑎 and 𝑏 are prime numbers.

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

Q8:

Write 3 4 3 × 3 × 3 4 3 × 3 2 3 4 4 in the form 𝑎 𝑏 𝑚 𝑛 where 𝑎 and 𝑏 are prime numbers.

  • A 3 4 3 × 3 1 8 7
  • B 7 × 3 6 7
  • C 3 4 3 × 3 7 6
  • D 7 × 3 1 8 7

Q9:

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

  • A 2 × 2 1 1
  • B 2 2 2
  • C 2 2 3
  • D 3 × 2 1 1
  • E 3 × 2 1 2

Q10:

Calculate − 1 1 9 − − 1 1 9 .

  • A − 1 8 6 , 8 5 9
  • B 2 0 6 , 8 5 9
  • C 1 8 6 , 8 5 9
  • D − 2 0 6 , 8 5 9

Q11:

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

Q12:

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

Q13:

Which of the following is equal to 2 − 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

Q14:

Simplify ( 2 5 ) × ( 8 ) ( 1 0 0 ) × √ 1 0 0 3 2 5 3 3 2 𝑥 𝑥 − 𝑥 .

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

Q15:

Determine the simplest form of ( 1 6 ) × 2 7 ( 1 4 4 ) × √ 8 1 3 2 1 3 3 2 𝑥 𝑥 − 𝑥 .

  • A3
  • B 1 3
  • C27
  • D 1 2 7

Q16:

Simplify ( 3 6 ) × 8 6 × ( 1 2 ) × √ 1 6 𝑥 + 𝑥 + 1 𝑥 − 1 𝑥 + 5 𝑥 − 1 1 2 .

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

Q17:

Simplify the expression 𝑡 𝑣 𝑡 𝑣 3 8 − 5 4 2 3 1 2 − 2 3 .

  • A 𝑡 𝑣 3 2 1 6
  • B 𝑡 𝑣 7 6 7 3 6
  • C 𝑡 𝑣 − 7 3 6 − 7 6
  • D 𝑡 𝑣 7 3 6 7 6
  • E 𝑡 𝑣 7 3 7 3

Q18:

Simplify the expression 𝑡 𝑣 𝑡 𝑣 − 3 8 5 4 − 2 3 − 1 2 .

  • A 𝑡 𝑣 7 4 7 4
  • B 𝑡 𝑣 7 4 7 2 4
  • C 𝑡 𝑣 − 7 2 7 − 7 4
  • D 𝑡 𝑣 7 2 4 7 4
  • E 𝑡 𝑣 2 4 7 4 7

Q19:

Which of the following is equal to − 2 1 4 3 ?

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

Q20:

Which of the following is equal to − 3 4 3 ?

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

Q21:

Which of the following is equal to ( − 3 ) × ( − 3 ) 3 4 ?

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

Q22:

Which of the following has the same value as 3 2 4 ?

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

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