New
New
Year 7

Power notation

I can understand and use correct notation for positive integer exponents.

New
New
Year 7

Power notation

I can understand and use correct notation for positive integer exponents.

Lesson details

Key learning points

  1. There is special notation for squares and cubes and each part can be named.
  2. Repeated multiplication of the same number can be written using integer exponents.
  3. Numbers written with positive integer exponents can be expressed as products of the base.
  4. Products that include repeated multiplication of different base numbers may be simplified using exponents.

Common misconception

When different bases are used student multiply the bases. e.g. 2 x 5^2 = 10^2

Calculate and compare the 2, 2 x 5^2 = 50 & 10^2 = 100

Keywords

  • Base - The base is the number or term that has been multiplied by itself.

  • Exponent - An integer exponent identifies how many times the base number has been multiplied by itself.

The Casio Classwiz 991 is the general calculator used in this lesson. For all levels of students, calculators can be used to identify if calculations are correct to support priority of operations and calculator skills.
Teacher tip

Equipment

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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6 Questions

Q1.
Which word best goes in the gaps? The __________ root of the perfect __________ is the integer that has been multiplied by itself and then itself again to give that perfect __________ number.
square
Correct answer: cube
array
product
Q2.
Complete the calculation: $$\sqrt{144} = $$
Correct Answer: 12, twelve
Q3.
Work out $$\sqrt[3]{1000}$$
1
Correct answer: 10
100
500
Q4.
Starting with smallest, put these roots in order of size.
1 - $$\sqrt{1}$$
2 - $$\sqrt[3]{64}$$
3 - $$\sqrt[3]{125}$$
4 - $$\sqrt{49}$$
5 - $$\sqrt{64}$$
6 - $$\sqrt{169}$$
Q5.
Find the closest integer to $$\sqrt{30}$$
4
Correct answer: 5
6
7
Q6.
Find the closest integer to $$\sqrt[3]{1100}$$
9
Correct answer: 10
11
12
13

6 Questions

Q1.
Here is $$4^5$$. What does this mean?
$$ 4 + 4 + 4 + 4 + 4$$
Correct answer: $$4\times4\times4\times4\times4$$
$$4\times5$$
4 lots of 5
Q2.
Here is $$2^3$$. What does the number 2 represent?
Correct answer: the base
the exponent
the factor
the multiple
the power
Q3.
Use exponents to simplify: $$2\times2\times2\times2\times2\times2\times2\times2\times2\times2$$
$$2\times10$$
Correct answer: $$2^{10}$$
$$10\times2$$
$$10^2$$
Q4.
Match each calculation with how it should be said out loud.
Correct Answer:$$5^2\times8^3$$,Five squared multiplied by eight cubed

Five squared multiplied by eight cubed

Correct Answer:$$6^2\times11^5$$,Six squared multiplied by eleven to the power of five

Six squared multiplied by eleven to the power of five

Correct Answer:$$5^2\times3^8$$,Five squared multiplied by three to the power of eight

Five squared multiplied by three to the power of eight

Correct Answer:$$6^2\times5^{11}$$,Six squared multiplied by five to the power of eleven

Six squared multiplied by five to the power of eleven

Correct Answer:$$5^3\times8^3$$,Five cubed multiplied by eight cubed

Five cubed multiplied by eight cubed

Q5.
Match each calculation written using exponents with its equivalent calculation.
Correct Answer:$$2^3\times3^4$$,$$2\times2\times2\times3\times3\times3\times3$$

$$2\times2\times2\times3\times3\times3\times3$$

Correct Answer:$$2^4\times3^2$$,$$2\times2\times2\times2\times3\times3$$

$$2\times2\times2\times2\times3\times3$$

Correct Answer:$$3^2\times4^4$$,$$3\times3\times4\times4\times4\times4$$

$$3\times3\times4\times4\times4\times4$$

Correct Answer:$$3^2\times4^3$$,$$3\times3\times4\times4\times4$$

$$3\times3\times4\times4\times4$$

Q6.
Starting with the smallest, put these numbers in ascending order of size.
1 - $$1^{10}$$
2 - $$2^3$$
3 - $$10^1$$
4 - $$4^2$$
5 - $$5^2$$
6 - $$10^2$$
7 - $$5^3$$