Lesson Worksheet: Powers and Exponents for Rational Numbers Mathematics

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In this worksheet, we will practice identifying the base and exponent in power formulas, writing them in exponential and expanded forms, and evaluating simple powers.

Q1:

What is 411×411×411×411×411×411×411?

  • A2811
  • B411
  • C411
  • D711
  • E411

Q2:

What terminology do we use to describe the 12 in the expression 12 and the 5 in the expression 12?

  • A12 is called the base of the expression, and 5 is called the exponent of the expression.
  • B5 is called the base of the expression, and 12 is called the exponent of the expression.

Q3:

What is the base in 23?

  • A32
  • B3
  • C2
  • D23
  • E4

Q4:

Find the value of −65, giving your answer in its simplest form.

  • A−6125
  • B−216125
  • C−185
  • D−2165
  • E−25

Q5:

The volume of a cube is 14 of a cubic unit. Express this as a product, evaluating the volume of the cube.

  • A4×4×4=64 cubic units
  • B4×4=16 cubic units
  • C14×14×14=164 of a cubic unit
  • D3×3×3=27 cubic units
  • E13×13×13=127 of a cubic unit

Q6:

Calculate −23×−98.

  • A−13
  • B3
  • C8
  • D13
  • E−3

Q7:

Evaluate the expression 23×65÷45, giving your answer as a fraction in simplest form.

  • A2524
  • B3275
  • C7532
  • D2425
  • E256625

Q8:

Find an expression for the volume of the given cube whose side lengths are 2𝑥5.

  • A4𝑥25
  • B8𝑥125
  • C8𝑥25
  • D8𝑥125
  • E4𝑥25

Q9:

If 𝑎=−23, 𝑏=13, and 𝑐=−92, find the numerical value of 𝑎𝑏𝑐.

Q10:

If 𝑥=32 and 𝑦=−45, find the value of 𝑥𝑦−𝑥𝑦, giving your answer as a fraction in simplest form.

  • A321125
  • B−129125
  • C129125
  • D−321125
  • E−125129

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