Worksheet: Simplifying Expressions: Rules of Exponents

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

Q1:

Factor out the greatest common factor to rewrite the expression 2−8.

  • A8(2−1)
  • B8(2−8)
  • C64(2−1)
  • D−8(2+1)
  • E−64(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.

  • A0.027𝑘
  • B0.027𝑘
  • C0.3𝑘
  • D0.27𝑘
  • E0.3𝑘

Q4:

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

  • A30(2), 45(3)
  • B2252, 3,3752
  • C152, 152
  • D225(2), 3,375(3)
  • E302, 452

Q5:

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

  • A𝑚=80, 𝑛=48
  • B𝑚=29, 𝑛=31
  • C𝑚=29, 𝑛=3
  • D𝑚=0, 𝑛=31
  • E𝑚=0, 𝑛=3

Q6:

Simplify 𝑥×𝑥𝑥×𝑥, where 𝑥≠0.

  • A𝑥
  • B𝑥
  • C𝑥
  • D𝑥

Q7:

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

  • A3𝑥𝑦
  • B18𝑥𝑦
  • C18𝑥𝑦
  • D12𝑥𝑦
  • E3𝑥𝑦

Q8:

Complete the following: −64𝑏=().

  • A−16𝑏
  • B4𝑏
  • C−4𝑏
  • D−4𝑏
  • E4𝑏

Q9:

Simplify 16𝑎8𝑎, leaving your answer in exponential form.

  • A12𝑎
  • B2𝑎
  • C2𝑎
  • D12𝑎
  • E2𝑎

Q10:

Simplify 29𝑎𝑏.

  • A29𝑎𝑏
  • B481𝑎𝑏
  • C481𝑎𝑏
  • D481𝑎𝑏
  • E29𝑎𝑏

Q11:

Complete the following: 14𝑥𝑦⋯=2𝑥6𝑦.

  • A6𝑥𝑦
  • B42𝑥𝑦
  • C12𝑥𝑦
  • D42𝑥𝑦

Q12:

Which of these equations is satisfied by 𝑥=23 and 𝑦=332−32?

  • A𝑥=𝑦
  • B𝑥=1𝑦
  • C𝑥=𝑦
  • D𝑥=1𝑦

Q13:

Given that 5=2, determine the value of 25.

Q14:

Given that 𝑧=−14, find the numerical value of (−8𝑧)×𝑧16𝑧.

  • A1128
  • B13
  • C−64
  • D−4
  • E18

Q15:

Simplify 𝑥×𝑥×𝑥𝑥×𝑥×𝑥.

  • A1𝑥
  • B𝑥
  • C𝑥
  • D𝑥

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