New
New
Year 10
Higher

The laws of indices - fractional exponents

I can use the laws of indices with fractional exponents.

New
New
Year 10
Higher

The laws of indices - fractional exponents

I can use the laws of indices with fractional exponents.

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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)

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.

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.

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).

Lesson video

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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

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