Lesson Worksheet: Simplifying Exponential Expressions with Rational Exponents Mathematics • 9th Grade

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In this worksheet, we will practice performing operations and simplifications with expressions that involve rational exponents.

Q1:

Simplify −64𝑎𝑏, where 𝑎 and 𝑏 are positive constants.

  • A(64)𝑎𝑏
  • B2𝑎𝑏
  • C−𝑎𝑏(64)
  • D−2𝑎𝑏
  • E−2𝑎𝑏

Q2:

Simplify (0.25)(1.8)8.

  • A81800
  • B162,000
  • C571,000
  • D10,125
  • E8150

Q3:

Simplify 𝑎×(𝑎)𝑎×(32𝑎), where 𝑎 is a positive constant and 𝑎≠1.

  • A𝑎
  • B2𝑎
  • C12𝑎
  • D12𝑎
  • E12𝑎

Q4:

Simplify 45×(63)×3225×(21).

  • A3
  • B3
  • C3
  • D9

Q5:

Determine the simplest form of (16)×27(144)×√81.

  • A127
  • B3
  • C13
  • D27

Q6:

Simplify 4×252×50.

  • A4
  • B256
  • C1256
  • D14

Q7:

Simplify (36)×86×(12)×√16.

  • A864
  • B216
  • C1216
  • D1864

Q8:

Expand −𝑎+1𝑎, where 𝑎 is a real constant.

  • A−𝑎−2𝑎−1𝑎
  • B−𝑎−1𝑎
  • C𝑎+2𝑎+1𝑎
  • D𝑎−2𝑎+1𝑎
  • E𝑎+1𝑎

Q9:

Simplify (0.8)×(36)×5(30)×(1.25).

  • A790
  • B1,012
  • C1,800
  • D141,000
  • E761,000

Q10:

Simplify (36)×(21)×(8)(486)×(42).

  • A184
  • B741,000
  • C84
  • D6,270
  • E411,000

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