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Year 10
Higher

The laws of indices - negative and zero exponents

I can use the laws of indices with negative and zero exponents.

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Year 10
Higher

The laws of indices - negative and zero exponents

I can use the laws of indices with negative and zero exponents.

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

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Lesson details

Key learning points

  1. A calculator can be helpful to explore what happens when the exponent is zero or negative.
  2. Any term with an exponent of zero is equal to one.
  3. A negative exponent tells you how many times you need to multiply the reciprocal of the base.
  4. Negative exponents appear when writing very small numbers in standard form.

Keywords

  • Reciprocal - A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

  • Indices - 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).

Common misconception

Any number with an index of 0 equates to 0

Reiterate the division of any number by itself is 1. This applies with laws of indices too. E.g 8^4 / 8^4 = 8^0. Any number divided by itself gives 1, therefore 8^0 = 1. For more advanced understanding, algebraic can be used instead of numbers.


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

Pupils create 5 of their own questions which give an answer of 5 using a range of operations and a term with an index of 0. For example, 9^0 x 5 = 5, 5x^0 = 5, 10x^0/2 = 5, etc
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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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Starter quiz

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6 Questions

Q1.
What is the value of $$x$$ for $$(m^x)^8 = m^{24}$$
Correct Answer: 3
Q2.
What is the value of $$x$$ for $$(m^5)^5 = m^x$$
Correct Answer: 25
Q3.
What is the value of $$x$$ for $$(m^3)^x = m^9$$
Correct Answer: 3
Q4.
What is the value of $$x$$ for $$(m^8)^3 = m^x$$
Correct Answer: 24
Q5.
What is the value of $$x$$ for $$\frac{1}{4} = \frac{1}{2^x}$$
Correct Answer: 2
Q6.
What is the value of $$x$$ for $$\frac{1}{64} = \frac{1}{2^x}$$
Correct Answer: 6

Exit quiz

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6 Questions

Q1.
What is the value of $$x$$ for $$(m^x)^{-8} = m^{24}$$
Correct Answer: -3
Q2.
What is the value of $$x$$ for $$(m^{-5})^5 = m^x$$
Correct Answer: -25
Q3.
What is the value of $$x$$ for $$(m^3)^x = m^{-3}$$
Correct Answer: -1
Q4.
What is the value of $$x$$ for $$\frac{1}{4} = 2^x$$
Correct Answer: -2
Q5.
What is the value of $$x$$ for $$\frac{1}{64} = 2^x$$
Correct Answer: -6
Q6.
What is the value of $$a$$ for $$5^8 \times 5^a = 5^6$$?
Correct Answer: -2