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Grade 10 · Core Mathematics · Lesson 1 of 13

Reading Repeated Factors as Indices

A Grade 10 Core Mathematics CBE lesson from the sub-strand Indices and Logarithms. In it, learners represent repeated multiplication with index notation.

Strand Numbers and AlgebraSub-strand Indices and LogarithmsLesson code 10CM-12-L140 minutes · 2 slides

KICD learning outcome (a)

Express numbers in index form.

By the end of this lesson, learners should be able to

  1. Represent repeated multiplication with index notation.
  2. Name the base and exponent accurately.
  3. Check an index form by expanding it.

Key vocabulary

Base
The repeated factor multiplied throughout an index expression.
In 4⁵, the base is four, repeated five times.
Exponent
The small raised number counting repeated factors.
The exponent three means three copies of the base occur.
Index form
A number written as a base raised to an exponent.
Twenty-five can be written as 5² in index form.
Factor
A number multiplied with another number to make a product.
Five is a factor of twenty-five because 5 × 5 equals 25.

Lesson preview

Slide 1 · From factors to a compact formOpening · 18 min
The image shows how the repeated multiplication of six, five times, is written in index notation with six as the base and five as the exponent.
Figure 1: The image shows how the repeated multiplication of six, five times, is written in index notation with six as the base and five as the exponent.

Index notation gives a short, readable way to record equal factors. The base is the repeated factor, while the exponent counts how many copies appear; neither part may be guessed from the final product alone. Study Figure 1 to see how the base and exponent identify the repeated factors and their count.

  • A base is the factor that repeats in the multiplication.
  • An exponent records the number of equal factors present.
  • Writing factors first helps prevent confusing base with exponent.
  • Expanding an index expression checks whether its value is sensible.
Worked example. Count the five equal factors. Use 6 as the base and 5 as the exponent. Write 6⁵ and expand it once to verify. Answer: 6⁵.

Check question: What index form represents 9 × 9 × 9?

Show answer

9³. There are three equal factors, so nine is the base and three is the exponent.

Slide 2 · Choosing a useful basePractice · 22 min
A factor tree breaks down the number 2,187 into seven repeated factors of three, which are then written and verified in index form.
Figure 2: A factor tree breaks down the number 2,187 into seven repeated factors of three, which are then written and verified in index form.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 12 lessons in this sub-strand
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All 13 lessons in Indices and Logarithms

  1. 1Reading Repeated Factors as IndicesExpress numbers in index form
  2. 2Index Forms with a Specified BaseExpress numbers in index form
  3. 3Discovering Product and Quotient LawsDerive the laws of indices using factors
  4. 4Power of a Power and Identity CasesDerive the laws of indices using factors
  5. 5Indices in Measurement and DesignApply the laws of indices in different situations
  6. 6From Powers of Ten to Common LogsRelate index notation to logarithm notation to base 10
  7. 7Interpreting Base-Ten LogarithmsRelate index notation to logarithm notation to base 10
  8. 8Reading Common Logarithms in TablesDetermine common logarithms of numbers from mathematical tables and calculators
  9. 9Comparing Table and Calculator LogarithmsDetermine common logarithms of numbers from mathematical tables and calculators
  10. 10Logarithms for Multiplication and DivisionApply common logarithms in multiplication, division, powers and roots of numbers
  11. 11Logarithms for Powers and RootsApply common logarithms in multiplication, division, powers and roots of numbers
  12. 12Integrated Logarithmic ComputationApply common logarithms in multiplication, division, powers and roots of numbers
  13. 13Why Indices and Logarithms MatterAppreciate the use of indices and common logarithms in mathematical computations