Lesson Worksheet: Simplifying Expressions: Rules of Exponents Mathematics • 10th Grade

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


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

  • A8(21)
  • B8(28)
  • C64(21)
  • D8(2+1)
  • E64(2+1)


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

  • A244
  • B489
  • C493
  • D245


Simplify 0.3𝑘.

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


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


Simplify 𝑥×𝑥𝑥×𝑥, where 𝑥0.

  • A𝑥
  • B𝑥
  • C𝑥
  • D𝑥


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


Complete the following: 64𝑏=().

  • A16𝑏
  • B4𝑏
  • C4𝑏
  • D4𝑏
  • E4𝑏


Simplify 16𝑎8𝑎, leaving your answer in exponential form.

  • A12𝑎
  • B2𝑎
  • C2𝑎
  • D12𝑎
  • E2𝑎


Simplify 29𝑎𝑏.

  • A29𝑎𝑏
  • B481𝑎𝑏
  • C481𝑎𝑏
  • D481𝑎𝑏
  • E29𝑎𝑏


Complete the following: 14𝑥𝑦=2𝑥6𝑦.

  • A6𝑥𝑦
  • B42𝑥𝑦
  • C12𝑥𝑦
  • D42𝑥𝑦

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