Worksheet: Simplifying Expressions Using the Laws of Indices

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In this worksheet, we will practice simplifying expressions using the rules of indices.

Q1:

Factor out the highest common factor to rewrite the expression 2 − 8 𝑦 + 3 .

  • A − 8 ( 2 + 1 ) 𝑦
  • B 6 4 ( 2 − 1 ) 𝑦
  • C − 6 4 ( 2 + 1 ) 𝑦
  • D 8 ( 2 − 1 ) 𝑦
  • E 8 ( 2 − 8 ) 𝑦

Q2:

Which of the following numbers is the expression 3 + 3 divisible by for all natural numbers 𝑥 ?

  • A489
  • B245
  • C493
  • D244

Q3:

Simplify 0 . 3 𝑘 2 3 .

  • A 0 . 3 𝑘 6
  • B 0 . 0 2 7 𝑘 5
  • C 0 . 3 𝑘 5
  • D 0 . 0 2 7 𝑘 6
  • E 0 . 2 7 𝑘 6

Q4:

Simplify the expressions [ 1 5 ( 2 ) ] 𝑥 2 and [ 1 5 ( 2 ) ] 𝑥 3 .

  • A 1 5 2 2 𝑥 , 1 5 2 3 𝑥
  • B 3 0 2 2 𝑥 , 4 5 2 3 𝑥
  • C 2 2 5 ( 2 ) 𝑥 , 3 3 7 5 ( 3 ) 𝑥
  • D 2 2 5 2 2 𝑥 , 3 3 7 5 2 3 𝑥
  • E 3 0 ( 2 ) 𝑥 , 4 5 ( 3 ) 𝑥

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