1. Powers and Square Roots

2. Powers Sometimes numbers multiply themselves a few times for example 3×3×3×3×3.

3. Powers Sometimes numbers multiply themselves a few times for example 3×3×3×3×3. Mathematicians try to find easier ways to write anything that takes a lot of space.

4. Powers Just like 3+3+3+3 is written 4 × 3, there is a shorter way to write 3 × 3 × 3 × 3.

5. Powers Just like 3+3+3+3 is written 4 × 3, there is a shorter way to write 3 × 3 × 3 × 3. This shorter way uses a special notation called powers (or exponents or indices).

6. Powers

8. Special Powers Any number raised to the power of 2 is said to have been “squared”

9. Special Powers Any number raised to the power of 2 is said to have been “squared” Any number raised to the power of 3 is said to have been “cubed”

10. Examples

11. How to undo Powers? The undoing process, or in mathematical language, the inverse process of finding the n th power of a number is to find the n th root of the answer.

12. How to undo Powers? The undoing process, or in mathematical language, the inverse process of finding the n th power of a number is to find the n th root of the answer. Note the inverse of squaring is square rooting and the inverse of cubing is cube rooting.

13. Examples

19. Expectations at Year 9 No calculators are allowed throughout this topic, so to perform square roots and cube roots, students should be familiar with square and cube numbers.

20. Expectations at Year 9 No calculators are allowed throughout this topic, so to perform square roots and cube roots, students should be familiar with square and cube numbers. Square Numbers1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 Cube Numbers1, 8, 27, 64, 125, 216, 343, 512, 729, 1000