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Worksheet: Simplifying Expressions Using the Laws of Indices

Q1:

Simplify the expressions [ 1 5 ( 2 ) ] π‘₯ 2 and [ 1 5 ( 2 ) ] π‘₯ 3 .

  • A 1 5 ο€Ή 2  2 π‘₯ , 1 5 ο€Ή 2  3 π‘₯
  • B 3 0 ο€Ή 2  2 π‘₯ , 4 5 ο€Ή 2  3 π‘₯
  • C 2 2 5 ( 2 ) π‘₯ , 3 3 7 5 ( 3 ) π‘₯
  • D 2 2 5 ο€Ή 2  2 π‘₯ , 3 3 7 5 ο€Ή 2  3 π‘₯
  • E 3 0 ( 2 ) π‘₯ , 4 5 ( 3 ) π‘₯

Q2:

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

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

Q3:

Which of the following numbers is the expression 3 + 3 π‘₯ + 5 π‘₯ divisible by for all natural numbers π‘₯ ?

  • A489
  • B245
  • C493
  • D244

Q4:

Simplify ο€Ή 0 . 3 π‘˜  2 3 .

  • A 0 . 3 π‘˜ 6
  • B 0 . 0 2 7 π‘˜ 5
  • C 0 . 3 π‘˜ 5
  • D 0 . 0 2 7 π‘˜ 6
  • E 0 . 2 7 π‘˜ 6