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Lesson 8 of 10
  • Year 10
  • Higher

The laws of indices - multiplication

I can use the laws of indices to multiply two powers where the bases are the same.

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Lesson 8 of 10
New
New
  • Year 10
  • Higher

The laws of indices - multiplication

I can use the laws of indices to multiply two powers where the bases are the same.

Download all
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. When multiplying two terms, you can sometimes write this more simply.
  2. If the powers have the same base, then the powers can be combined into a single power.
  3. The exponent or index of the new power reflects this combination.
  4. By studying the structure of multiplication, you can see how the index will change.
  5. a^b × a^c = a^(b+c)

Keywords

  • Power - 16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as “2 to the power of 4”.

  • Index - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).

  • Coefficient - A numerical coefficient is a constant multiplier of the variables in a term.

  • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

  • Associative - An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.

Common misconception

When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.

Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.


To help you plan your year 10 maths lesson on: The laws of indices - multiplication, download all teaching resources for free and adapt to suit your pupils' needs...

When changing the base, quick recall of powers of 2, 3, 4, 5 and 10 are useful. Using MWB you call out a number and the pupils write it as a power. This could also be done as a bingo game.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Calculate $$-3 \times 5^2$$

Correct Answer: -75

Q2.
Calculate $$-3 \times 4^2$$

Correct Answer: -48

Q3.
Calculate $$-3 \times 2^2$$

Correct Answer: -12

Q4.
Calculate $$-4 \times 4^2$$

Correct Answer: -64

Q5.
Calculate $$3^2 + (-4)^2$$

Correct Answer: 25

Q6.
Calculate $$9^2 + (-5)^2$$

Correct Answer: 106

Assessment exit quiz

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6 Questions

Q1.
What is the value of $$a$$ for $$3^3 \times 3^a = 3^{20}$$?

Correct Answer: 17

Q2.
What is the value of $$a$$ for $$3^3 \times 3^a = 3^7$$?

Correct Answer: 4

Q3.
What is the value of $$a$$ for $$5^8 \times 5^a = 5^{10}$$?

Correct Answer: 2

Q4.
What is the value of $$a$$ for $$3^3 \times a^7 = 3^{10}$$?

Correct Answer: 3

Q5.
What is the value of $$a$$ for $$3^7 \times a^8 = 3^{15}$$?

Correct Answer: 3

Q6.
What is the value of $$a$$ for $$6^3 \times 6^8 = 6^a$$?

Correct Answer: 11