Worksheet: Simplifying Expressions: Rules of Exponents

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

Q1:

Factor out the highest common factor to rewrite the expression 28.

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

Q2:

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

  • A244
  • B489
  • C493
  • D245

Q3:

Simplify 0.3𝑘.

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

Q4:

Simplify the expressions [15(2)] and [15(2)].

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

Q5:

If 45𝑥𝑦 and 35𝑥𝑦 are like terms, what are the values of 𝑚 and 𝑛?

  • A 𝑚 = 8 0 , 𝑛 = 4 8
  • B 𝑚 = 0 , 𝑛 = 3 1
  • C 𝑚 = 2 9 , 𝑛 = 3 1
  • D 𝑚 = 2 9 , 𝑛 = 3
  • E 𝑚 = 0 , 𝑛 = 3

Q6:

Simplify 𝑥×𝑥𝑥×𝑥, where 𝑥0.

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥

Q7:

Given that 𝐴𝐷=𝑥𝑦cm and 𝐶𝐵=6𝑥𝑦cm, determine, in its simplest form, the algebraic expression that represents the area of triangle 𝐴𝐵𝐶.

  • A 3 𝑥 𝑦
  • B 1 8 𝑥 𝑦
  • C 1 8 𝑥 𝑦
  • D 1 2 𝑥 𝑦
  • E 3 𝑥 𝑦

Q8:

Complete the following: 64𝑏=().

  • A 1 6 𝑏
  • B 4 𝑏
  • C 4 𝑏
  • D 4 𝑏
  • E 4 𝑏

Q9:

Simplify 16𝑎8𝑎, leaving your answer in exponential form.

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

Q10:

Simplify 29𝑎𝑏.

  • A 2 9 𝑎 𝑏
  • B 4 8 1 𝑎 𝑏
  • C 4 8 1 𝑎 𝑏
  • D 4 8 1 𝑎 𝑏
  • E 2 9 𝑎 𝑏

Q11:

Complete the following: 14𝑥𝑦=2𝑥6𝑦.

  • A 6 𝑥 𝑦
  • B 4 2 𝑥 𝑦
  • C 1 2 𝑥 𝑦
  • D 4 2 𝑥 𝑦

Q12:

Which of these equations is satisfied by 𝑥=23 and 𝑦=33232?

  • A 𝑥 = 𝑦
  • B 𝑥 = 1 𝑦
  • C 𝑥 = 𝑦
  • D 𝑥 = 1 𝑦

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