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Year 10
Higher

The laws of indices - fractional exponents

I can use the laws of indices with fractional exponents.

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New
New
Year 10
Higher

The laws of indices - fractional exponents

I can use the laws of indices with fractional exponents.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. All of the index laws can be applied with fractional exponents.
  2. Using a calculator can help you to form an idea about how to evaluate a power containing a fractional exponent.
  3. You can reason that a power with a fractional exponent is equivalent to finding the square root of the base.
  4. √a = a^(1/2)

Common misconception

Pupils multiply the base by the fractional exponent. e.g 25^(1/2) = 12.5

The use of a calculator allows pupils to see the index of a fraction is not to be multiplied by the base. Embedding the laws of indices where two bases are the same and each number has an index of 1/2 helps recognize the 1/2 index as a square root.

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.

Using MWB, put the number 100 in the centre. Pupils must create as many numbers with an exponent that equate to 10. E.g 10^2, (1/100)^-1, 1000^(2/3), 4x125^(2/3), etc. Display the summary of the laws of indices to helps and give access to calculators for more support.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
What is the value of $$x$$ for $$(m^x)^8 = m^{32}$$
Correct Answer: 4
Q2.
What is the value of $$x$$ for $$(m^{-2})^5 = m^x$$
Correct Answer: -10
Q3.
What is the value of $$x$$ for $$(m^8)^x = m^{80}$$
Correct Answer: 10
Q4.
What is the value of $$x$$ for $$\frac{1}{16} = 2^x$$
Correct Answer: -4
Q5.
What is the value of $$x$$ for $$\frac{1}{64} = x^{-6}$$
Correct Answer: 2
Q6.
What is the value of $$a$$ for $$7^9 \times 7^a = 7^6$$?
Correct Answer: -3

Exit quiz

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6 Questions

Q1.
Evaluate $$36^{\frac{1}{2}}$$, giving the positive solution where necessary.
Correct Answer: 6
Q2.
Evaluate $$1000^{\frac{1}{3}}$$, giving the positive solution where necessary.
Correct Answer: 10
Q3.
Evaluate $$27^{\frac{2}{3}}$$, giving the positive solution where necessary.
Correct Answer: 9
Q4.
Evaluate $$1000^{\frac{2}{3}}$$, giving the positive solution where necessary.
Correct Answer: 100
Q5.
Evaluate $$16^{\frac{3}{4}}$$, giving the positive solution where necessary.
Correct Answer: 8
Q6.
Evaluate $$16^{\frac{3}{2}}$$, giving the positive solution where necessary.
Correct Answer: 64