Worksheet: Simplifying Expressions Using Rules of Negative and Fractional Exponents

In this worksheet, we will practice using the rules of negative and fractional indices to solve problems.

Q1:

Express 1 5 ๐‘ฅ โˆ’ 6 1 9 in the form ๐‘Ž โˆš ๐‘ ๐‘ฅ ๐‘š ๐‘› .

  • A 6 โˆš 1 5 ๐‘ฅ 1 9
  • B 1 9 โˆš 1 5 ๐‘ฅ 6
  • C 1 5 โˆš ๐‘ฅ 6 1 9
  • D 1 5 โˆš ๐‘ฅ 1 9 6
  • E 1 โˆš 1 5 ๐‘ฅ 1 9 6

Q2:

Which of the following is equal to ๏€ป ๏‡ ร— ๏€ป ๏‡ ๏€ป ๏‡ ๏Šฉ ๏Šซ ๏Šฑ ๏Šฌ ๏Šฉ ๏Šซ ๏Šฑ ๏Šฉ ๏Šฉ ๏Šซ ๏Šฎ ?

  • A ๏€ผ 3 5 ๏ˆ ๏Šฑ ๏Šจ ๏Šซ
  • B ๏€ผ 3 5 ๏ˆ ๏Šฑ ๏Šง
  • C ๏€ผ 3 5 ๏ˆ ๏Šง ๏Šง
  • D ๏€ผ 3 5 ๏ˆ ๏Šฑ ๏Šง ๏Šญ
  • E ๏€ผ 3 5 ๏ˆ ๏Šฑ ๏Šง ๏Šง

Q3:

Simplify 6 ร— 3 2 ๏Šฑ ๏Šฉ ๏Šฑ ๏Šง .

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

Q4:

Simplify ๏€น โˆ’ 5 ๐‘š ๏… ๏€น โˆ’ 7 ๐‘š ๏… ๏Šฏ ๏Šญ .

  • A โˆ’ 3 5 ๐‘š ๏Šจ
  • B โˆ’ 3 5 ๐‘š ๏Šฌ ๏Šฉ
  • C โˆ’ 7 ๐‘š ๏Šง ๏Šฌ
  • D 3 5 ๐‘š ๏Šง ๏Šฌ
  • E 3 5 ๐‘š ๏Šฌ ๏Šฉ

Q5:

Evaluate 0 . 2 0 .

Q6:

Evaluate 8 โ‹… 6 โ‹… 3 ๏Šจ ๏Šฑ ๏Šซ .

  • A 4 2 7
  • B 2 5 6 2 7
  • C54
  • D 3 2 2 7
  • E 2 7 4

Q7:

If the expression ๏€ผ 2 3 ๏ˆ โˆ’ 2 ๐‘ฆ is rewritten in the form ๐‘ƒ ๐‘ฆ , what is the value of ๐‘ƒ ?

  • A ๏€ผ 4 3 ๏ˆ
  • B ๏€ผ 2 3 ๏ˆ 2
  • C ๏€ผ 4 3 ๏ˆ โˆ’ 1
  • D ๏€ผ 3 2 ๏ˆ 2
  • E ๏€ผ 9 2 ๏ˆ

Q8:

Simplify ๏€ป โˆš 8 ๏‡ ๏Šฑ ๏Šจ .

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

Q9:

Which of the following is equal to ๏€ป โˆš 6 ๏‡ ๏Šช ?

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

Q10:

Find the value of ๏€ป โˆš 9 ๏‡ ๏Žก ๏Žข ๏Žก ๏Žข ๏Ž  ๏Žฃ ๏Šจ ๏Šฎ .

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

Q11:

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

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

Q12:

Simplify ๏€ผ ๐‘š ๐‘› ๏ˆ ๏€พ 2 ๐‘š ๐‘› ๏Š ๏Šฑ ๏Šง ๏Šฑ ๏Šฉ ๏Šฑ ๏Šจ ๏Šฑ ๏Šจ ๏Šฑ ๏Šฉ .

  • A 1 8 ๐‘š ๐‘› ๏Šฏ ๏Šฏ
  • B 8 ๐‘š ๐‘› ๏Šฉ ๏Šฏ
  • C ๐‘š ๐‘› 8 ๏Šฉ ๏Šฉ
  • D ๐‘š 8 ๐‘› ๏Šฉ ๏Šฏ
  • E 8 ๐‘š ๐‘› ๏Šฏ ๏Šฉ

Q13:

Which of the following is equal to โˆ’ 1 0 9 ๐‘ฅ ๐‘ฆ ๏Šฑ ๏Šจ ๏Šฑ ๏Šญ ?

  • A โˆ’ 1 0 9 ๐‘ฅ ๐‘ฆ ๏Šญ ๏Šจ
  • B โˆ’ 9 1 0 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šญ
  • C โˆ’ 1 0 ๐‘ฅ ๐‘ฆ 9 ๏Šจ ๏Šญ
  • D โˆ’ 1 0 9 ๐‘ฅ ๐‘ฆ ๏Šจ ๏Šญ

Q14:

Evaluate ๏€ผ 6 4 2 7 ๏ˆ โˆ’ 2 3 .

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

Q15:

Let ๐‘ฅ = ๏„ก ๏„ฃ ๏„ฃ ๏„  โˆš 7 โˆš 2 ๏Žค ๏Žข ๏Žฃ . Which of the following numbers is rational?

  • A ๐‘ฅ ๏Šฉ
  • B ๐‘ฅ ๏Šง ๏Šจ
  • C ๐‘ฅ ๏Šง ๏Šซ
  • D ๐‘ฅ ๏Šฌ ๏Šฆ
  • E ๐‘ฅ ๏Šช

Q16:

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

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

Q17:

Which of the following is equal to ( โˆ’ 3 ) ร— ( โˆ’ 3 ) โˆ’ 5 4 ?

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

Q18:

Which of the following expressions has the same value as ๏€น 3 ๏… 2 โˆ’ 4 ?

  • A 3 โˆ’ 2
  • B 3 8
  • C โˆ’ 3 8
  • D ๏€ผ 1 9 ๏ˆ 4
  • E ๏€ผ 1 3 ๏ˆ 2

Q19:

Which of the following expressions has the same value as ๏€น ( โˆ’ 2 ) ๏… โˆ’ 8 โˆ’ 6 ?

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

Q20:

Which of the following expressions has the same value as ๏€พ ๏€ผ โˆ’ 3 4 ๏ˆ ๏Š 5 โˆ’ 7 ?

  • A ๏€ผ 4 3 ๏ˆ 3 5
  • B ๏€ผ 3 4 ๏ˆ 3 5
  • C ๏€ผ โˆ’ 4 3 ๏ˆ 1 2
  • D ๏€ผ โˆ’ 4 3 ๏ˆ 3 5
  • E ๏€ผ 3 4 ๏ˆ 1 2

Q21:

Which of the following is equal to ๏€ผ 1 3 5 ๏ˆ ร— ๏€ผ 1 3 5 ๏ˆ 2 โˆ’ 3 ?

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

Q22:

Which of the following expressions has the same value as ๏€พ ๏€ผ โˆ’ 3 4 ๏ˆ ๏Š โˆ’ 3 6 ?

  • A ๏€ผ โˆ’ 3 4 ๏ˆ โˆ’ 9
  • B ๏€ผ โˆ’ 3 4 ๏ˆ 1 8
  • C ๏€ผ โˆ’ 3 4 ๏ˆ 9
  • D ๏€ผ โˆ’ 3 4 ๏ˆ โˆ’ 1 8
  • E ๏€ผ โˆ’ 3 4 ๏ˆ 3

Q23:

Which of the following is equal to ๏€ผ โˆ’ 3 1 2 ๏ˆ โˆ’ 2 ?

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

Q24:

Which of the following expressions has the same value as ๏€บ ( โˆ’ 2 ) ๏† 5 โˆ’ 3 ?

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

Q25:

Which of the following is equal to ๏€ผ 3 4 ๏ˆ ร— ๏€ผ 3 4 ๏ˆ 2 โˆ’ 3 ?

  • A 3 4
  • B 5 4 5 1 7 2 9
  • C 9 1 6
  • D 1 1 3
  • E 2 4 3 1 0 2 4

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