2E Using indices

Learning intentions for this section:

• To know the meaning of the terms power, exponent, base and index

• To be able to write a product in index form if there are repeated factors

• To be able to evaluate expressions involving powers of known numbers

Past, present and future learning:

• The concepts in this section may be new to students

• This section prepares students for future work in algebra

When repeated multiplication of a number occurs, the expression can be simplified using powers. This involves writing the repeated factor as the base number and then including an index number to indicate how many times this factor must be multiplied by itself. This is also known as writing a number in index form. For example, 2 × 2 × 2 can be written as 23. The base number is 2 and the index number is 3

Powers are also used to represent very large and very small numbers. For example, 400000000000000 would be written as 4 × 1014. This way of writing a number is called standard form or scientific notation, as there are some very large numbers involved in science.

Lesson starter: A better way …

• What is a better way of writing the calculation

103 seconds ≈ 17minutes; 106 seconds ≈ 12 days; 109 seconds ≈ 32years 1012 secondsago ≈ 31710 years ago, before any written language, before the pyramids of Egypt, and when prehistoric artists painted the walls of Chauvet Cave, France.

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 (that is not the answer, 20)?

• What is a better way of writing the calculation

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 (that is not the answer, 1024)?

You may need to access the internet to find out some of the following answers.

Computers have the capacity to store a lot of information. As you most likely know, computer memory is given in bytes.

• How many bytes (B) are in a kilobyte (kB)?

• How many kilobytes are in a megabyte (MB)?

• How many megabytes are in a gigabyte (GB)?

• How many gigabytes are in a terabyte (TB)?

• How many bytes are in a gigabyte?