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Worksheet: Simplifying Expressions Using Rules of Negative and Fractional Exponents

Q1:

Express 1 5 π‘₯ βˆ’ 6 1 9 in the form π‘Ž √ 𝑏 π‘₯ π‘š 𝑛 .

  • A 6 √ 1 5 π‘₯ 1 9
  • B 1 9 √ 1 5 π‘₯ 6
  • C 1 5 √ π‘₯ 6 1 9
  • D 1 5 √ π‘₯ 1 9 6
  • E 1 √ 1 5 π‘₯ 1 9 6

Q2:

Evaluate .

  • A
  • B
  • C54
  • D
  • E

Q3:

Which of the following has the same value as 3 Γ· 3 2 βˆ’ 4 ?

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

Q4:

Evaluate ο€Ό 6 4 2 7  βˆ’ 2 3 .

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

Q5:

Let π‘₯ = ο„‘ ο„£ ο„£ ο„  √ 7 √ 2 5 3 4 . Which of the following numbers is rational?

  • A π‘₯ 3
  • B π‘₯ 1 2
  • C π‘₯ 1 5
  • D π‘₯ 6 0
  • E π‘₯ 4

Q6:

If the expression ο€Ό 2 3  βˆ’ 2 𝑦 is rewritten in the form 𝑃 𝑦 , what is the value of 𝑃 ?

  • A ο€Ό 4 3 
  • B ο€Ό 2 3  2
  • C ο€Ό 4 3  βˆ’ 1
  • D ο€Ό 3 2  2
  • E ο€Ό 9 2 

Q7:

Which of the following is equal to ( βˆ’ 3 ) Γ— ( βˆ’ 3 ) βˆ’ 5 4 ?

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

Q8:

Find the value of ο€» √ 9  2 3 2 3 1 4 2 8 .

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

Q9:

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

  • A 3 βˆ’ 2
  • B 3 8
  • C βˆ’ 3 8
  • D ο€Ό 1 9  4
  • E ο€Ό 1 3  2

Q10:

Which of the following expressions has the same value as ο€Ή ( βˆ’ 2 )  βˆ’ 8 βˆ’ 6 ?

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

Q11:

Simplify ο€Ό π‘š 𝑛  ο€Ύ 2 π‘š 𝑛  βˆ’ 1 βˆ’ 3 βˆ’ 2 βˆ’ 2 βˆ’ 3 .

  • A 1 8 π‘š 𝑛 9 9
  • B 8 π‘š 𝑛 3 9
  • C π‘š 𝑛 8 3 3
  • D π‘š 8 𝑛 3 9
  • E 8 π‘š 𝑛 9 3

Q12:

Simplify ο€Ή βˆ’ 5 π‘š  ο€Ή βˆ’ 7 π‘š  9 7 .

  • A βˆ’ 3 5 π‘š 2
  • B βˆ’ 3 5 π‘š 6 3
  • C βˆ’ 7 π‘š 1 6
  • D 3 5 π‘š 1 6
  • E 3 5 π‘š 6 3

Q13:

Which of the following expressions has the same value as ο€Ύ ο€Ό βˆ’ 3 4   5 βˆ’ 7 ?

  • A ο€Ό 4 3  3 5
  • B ο€Ό 3 4  3 5
  • C ο€Ό βˆ’ 4 3  1 2
  • D ο€Ό βˆ’ 4 3  3 5
  • E ο€Ό 3 4  1 2

Q14:

Which of the following is equal to βˆ’ 1 0 9 π‘₯ 𝑦 βˆ’ 2 βˆ’ 7 ?

  • A βˆ’ 1 0 9 π‘₯ 𝑦 7 2
  • B βˆ’ 9 1 0 π‘₯ 𝑦 2 7
  • C βˆ’ 1 0 π‘₯ 𝑦 9 2 7
  • D βˆ’ 1 0 9 π‘₯ 𝑦 2 7

Q15:

Which of the following is equal to ο€Ό 1 3 5  Γ— ο€Ό 1 3 5  2 βˆ’ 3 ?

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

Q16:

Which of the following is equal to ο€» √ 6  4 ?

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

Q17:

Which of the following expressions has the same value as ο€Ύ ο€Ό βˆ’ 3 4   βˆ’ 3 6 ?

  • A ο€Ό βˆ’ 3 4  βˆ’ 9
  • B ο€Ό βˆ’ 3 4  1 8
  • C ο€Ό βˆ’ 3 4  9
  • D ο€Ό βˆ’ 3 4  βˆ’ 1 8
  • E ο€Ό βˆ’ 3 4  3

Q18:

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

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

Q19:

Which of the following expressions is equal to ( βˆ’ 2 ) Γ— ( βˆ’ 2 ) βˆ’ 8 βˆ’ 6 ?

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

Q20:

Simplify ο€» √ 8  βˆ’ 2 .

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

Q21:

Simplify ο€» √ 2  3 βˆ’ 6 .

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

Q22:

Which of the following is equal to ο€»  Γ— ο€»  ο€»  3 5 βˆ’ 6 3 5 βˆ’ 3 3 5 8 ?

  • A ο€Ό 3 5  βˆ’ 2 5
  • B ο€Ό 3 5  βˆ’ 1
  • C ο€Ό 3 5  1 1
  • D ο€Ό 3 5  βˆ’ 1 7
  • E ο€Ό 3 5  βˆ’ 1 1

Q23:

Simplify 6 Γ— 3 2 βˆ’ 3 βˆ’ 1 .

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

Q24:

Evaluate 0 . 2 0 .

Q25:

Which of the following expressions has the same value as ο€Ί ( βˆ’ 2 )  5 βˆ’ 3 ?

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