Indices: powers of 2, 3, 5 and 10
Choose a base and an index, see the power written as repeated multiplication, and find its value. Discover what an index of 0 or 1 means, and why powers of 10 make place value.
Core concept
In short: See how 2³ means 2 × 2 × 2, and how fast powers grow.
A power such as 2³ means the base 2 multiplied by itself 3 times: 2 × 2 × 2 = 8; the index tells how many times; any base to the power 1 is itself, and to the power 0 is 1
Topic: Indices
Writing 2 × 2 × 2 × 2 × 2 takes a long time. Mathematicians write it as 2⁵, read “2 to the power 5”. The 2 is the base, the number multiplied, and the small raised 5 is the index (or exponent), the number of times it is multiplied. So 2⁵ = 32. Squares and cubes are powers too: 3² = 9 and 3³ = 27. Powers of 10 build our place value: 10¹ = 10, 10² = 100, 10³ = 1000, and 10⁶ is ten lakh, a million. Any base to the power 1 is just itself, and any base to the power 0 is 1.
What you will learn
- Identify the base and the index of a power.
- Write a power as repeated multiplication and find its value.
- Use powers of 10 in place value.
- State the value of a power with index 0 and 1.
Before you start
- Know the multiplication tables.
Materials
- A sheet of paper to fold in half again and again
Equipment
- A calculator to check
Procedure
- Record 2³.
- Record four or more powers of 2.
- Record 10³ and 10⁶.
- Record a power with index 0.
How this simulation is simplified
- The index is a whole number from 0 to 6.