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Worksheet: Using Rules of Negative and Fractional Exponents to Simplify Expressions

Q1:

Which of the following is equal to × 3 5 6 3 5 3 3 5 8 ?

  • A 3 5 2 5
  • B 3 5 1
  • C 3 5 1 1
  • D 3 5 1 7
  • E 3 5 1 1

Q2:

Simplify 6 × 3 2 3 1 .

  • A 4 3
  • B 324
  • C 36
  • D 1 3 6
  • E 432

Q3:

Simplify 5 𝑚 7 𝑚 9 7 .

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

Q4:

Evaluate 0 . 2 0 .

Q5:

Evaluate .

  • A
  • B
  • C54
  • D
  • E

Q6:

If the expression 2 3 2 𝑦 is rewritten in the form 𝑃 𝑦 , what is the value of 𝑃 ?

  • A 4 3
  • B 2 3 2
  • C 4 3 1
  • D 3 2 2
  • E 9 2

Q7:

Simplify 8 2 .

  • A 1 8
  • B 8
  • C 64
  • D 1 8
  • E 8

Q8:

Simplify 2 3 6 .

  • A 1 2
  • B 1 2
  • C 1 4
  • D 1 4
  • E 4

Q9:

Which of the following is equal to 6 4 ?

  • A 6
  • B 3 6 6
  • C 6
  • D 36
  • E 1 296

Q10:

Express 1 5 𝑥 6 1 9 in the form 𝑎 𝑏 𝑥 𝑚 𝑛 .

  • A 6 1 5 𝑥 1 9
  • B 1 9 1 5 𝑥 6
  • C 1 5 𝑥 6 1 9
  • D 1 5 𝑥 1 9 6
  • E 1 1 5 𝑥 1 9 6

Q11:

Find the value of 9 2 3 2 3 1 4 2 8 .

  • A 8 1
  • B1
  • C 1
  • D81
  • E 1 8 1

Q12:

Which of the following expressions is equal to ( 2 ) × ( 2 ) 8 6 ?

  • A 2 1 4
  • B ( 2 ) 4 8
  • C 2 1 4
  • D 2 1 4
  • E 4 1 4

Q13:

Simplify 𝑚 𝑛 2 𝑚 𝑛 1 3 2 2 3 .

  • A 1 8 𝑚 𝑛 9 9
  • B 8 𝑚 𝑛 3 9
  • C 𝑚 𝑛 8 3 3
  • D 𝑚 8 𝑛 3 9
  • E 8 𝑚 𝑛 9 3

Q14:

Which of the following is equal to 1 0 9 𝑥 𝑦 2 7 ?

  • A 1 0 9 𝑥 𝑦 7 2
  • B 9 1 0 𝑥 𝑦 2 7
  • C 1 0 𝑥 𝑦 9 2 7
  • D 1 0 9 𝑥 𝑦 2 7

Q15:

Evaluate 6 4 2 7 2 3 .

  • A 3 1 6
  • B 1 6 9
  • C 9 4
  • D 9 1 6
  • E 3 4

Q16:

Let 𝑥 = 7 2 5 3 4 . Which of the following numbers is rational?

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

Q17:

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

  • A 1 2
  • B 3 1 2
  • C 3 6
  • D 3 6
  • E 1 6

Q18:

Which of the following is equal to ( 3 ) × ( 3 ) 5 4 ?

  • A 1 3
  • B ( 3 ) 2 0
  • C 3
  • D 1 3
  • E 1 9

Q19:

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

  • A 3 2
  • B 3 8
  • C 3 8
  • D 1 9 4
  • E 1 3 2

Q20:

Which of the following expressions has the same value as ( 2 ) 8 6 ?

  • A ( 2 ) 1 4
  • B ( 2 ) 4 8
  • C 2 1 4
  • D ( 2 ) 4 8
  • E 2 4 8

Q21:

Which of the following expressions has the same value as 3 4 5 7 ?

  • A 4 3 3 5
  • B 3 4 3 5
  • C 4 3 1 2
  • D 4 3 3 5
  • E 3 4 1 2

Q22:

Which of the following is equal to 1 3 5 × 1 3 5 2 3 ?

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

Q23:

Which of the following expressions has the same value as 3 4 3 6 ?

  • A 3 4 9
  • B 3 4 1 8
  • C 3 4 9
  • D 3 4 1 8
  • E 3 4 3

Q24:

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

  • A 6 1 2
  • B 3 1 4
  • C 4 9 4
  • D 4 4 9
  • E 1 4 4

Q25:

Which of the following expressions has the same value as ( 2 ) 5 3 ?

  • A 1 2 8
  • B 2 1 5
  • C 2 8
  • D 1 2 1 5
  • E 2 2