Lesson Worksheet: Simplifying Exponential Expressions with Rational Exponents Mathematics

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

Q1:

Simplify (25)×(8)(100)×100.

  • A516
  • B1320
  • C320
  • D165

Q2:

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

  • A127
  • B3
  • C13
  • D27

Q3:

Simplify (36)×86×(12)×16.

  • A864
  • B216
  • C1216
  • D1864

Q4:

Simplify 4×252×50.

  • A4
  • B256
  • C1256
  • D14

Q5:

Simplify 45×(63)×3225×(21).

  • A3
  • B3
  • C3
  • D9

Q6:

Simplify 2×302×6×5.

  • A6,9125
  • B5216
  • C56,912
  • D2165

Q7:

Simplify 125×2525×5.

  • A150
  • B1150
  • C3,125
  • D13,125

Q8:

Simplify 𝑎+𝑎+𝑎𝑎+𝑎+𝑎.

  • A𝑎
  • B𝑎
  • C1
  • D𝑎
  • E𝑎𝑥

Q9:

Calculate 7×59×53×55, giving your answer in its simplest form.

  • A1097
  • B53
  • C514
  • D5
  • E2183

Q10:

Simplify 2×36 and evaluate this expression when 𝑥=2.

  • A2×3, 12
  • B2×3, 54
  • C2×3, 12
  • D2×3, 54
  • E2×3, 54

Q11:

Simplify 6×954.

Q12:

Simplify 256×1664×64.

  • A1128
  • B18
  • C12,048
  • D12

Q13:

What is the value of 2×48?

Q14:

Simplify 15×273×5, and evaluate this expression when 𝑛=2.

  • A3, 19
  • B3, 1
  • C3, 181
  • D3, 9

Q15:

Simplify 2×𝑛+5×𝑛(2𝑛+5𝑛), 𝑛.

  • A2𝑛+5𝑛49
  • B𝑛+𝑛
  • C149
  • D1
  • E2𝑛+5𝑛49

Q16:

Simplify (8)×0.64(0.2).

Q17:

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

  • A𝑎2𝑎1𝑎
  • B𝑎1𝑎
  • C𝑎+2𝑎+1𝑎
  • D𝑎2𝑎+1𝑎
  • E𝑎+1𝑎

Q18:

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

  • A(64)𝑎𝑏
  • B2𝑎𝑏
  • C𝑎𝑏(64)
  • D2𝑎𝑏
  • E2𝑎𝑏

Q19:

Simplify (0.8)×(36)×5(30)×(1.25).

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

Q20:

Simplify (36)×(21)×(8)(486)×(42).

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

Q21:

Simplify (0.25)(1.8)8.

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

Q22:

Fill in the blank: The expression (27)×(6)(0.09) can be written as .

  • A3×2×5
  • B3×2×5
  • C3×2×5
  • D3×2×5
  • E3×2×5

Q23:

Simplify 3𝑎𝑏𝑐.

  • A3𝑎𝑏𝑐
  • B9𝑎𝑏𝑐
  • C9𝑎𝑏𝑐
  • D243𝑎𝑏𝑐
  • E9𝑎𝑏𝑐

Q24:

For the expression 𝑥×𝑥𝑥×𝑥, 𝑥.

Write this expression in the form 𝑥, where 𝑎 is a function written in terms of 𝑛.

  • A𝑥
  • B𝑥
  • C𝑥
  • D𝑥
  • E𝑥

Evaluate this expression when 𝑥=2 and 𝑛=126. Round your answer to two decimal places if needed.

Q25:

Simplify 𝑎×(𝑎)𝑎×(32𝑎), where 𝑎 is a positive constant and 𝑎1.

  • A𝑎
  • B2𝑎
  • C12𝑎
  • D12𝑎
  • E12𝑎

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