1. Numbers Multiplying and Dividing by Powers

2. Numbers Any number (or letter) multiplied by itself will result in a square number. 2 x 2 = 4, 5 x 5 = 25 We call it a square number because …

3. Numbers …the area of a square is the length multiplied by the width, and these are always the same…obviously! 2cm x 2cm = 4cm 2 2cm

4. Numbers Instead of writing 2 x 2 (or the answer 4), in maths we write a number that is going to be squared like this:2 We call this the BASE number

5. Numbers Instead of writing 2 x 2 (or the answer 4), in maths we write a number that is going to be squared like this:2 And we call this the POWER or INDICES

6. Numbers The same is true in algebra. When we need to multiply a letter by itself instead of writing a x a we write a2a2

7. Numbers If we have to multiply a number by itself 3 times, or 4 times, then the small number (the power or indices) increases to show us how many times we multiply the number by itself… 4 x 4 x 4 = 7 x 7 x 7 x 7 x 7 x 7 = 4343 7676

8. Numbers g x g x g = g 3 What happens if we multiply g 3 by g 2 ? Do we get… IT ALL GETS SO CONFUSING!!!! g5g5 or2g 6 or2g 5 org6g6

9. Numbers We need to understand how this works g 3 = g x g x g g 2 = g x g So g 3 x g 2 is the same as g x g x g x g x g Which is… g5g5

10. Numbers From this we can now say that when we multiply power numbers we add the indices together: 2 4 x 2 8 = 3 3 x 3 5 = t 2 x t 8 = 2 12 3838 t 10

11. Numbers If we add indices when we multiply power numbers, what do we do when we divide power numbers? Subtract the indices! 2 8 ÷ 2 2 = 3 9 ÷ 3 4 = T 6 ÷ t 4 = 2626 3535 t2t2

12. Numbers Just two things to be careful of. 1)y x y 4 = y 5 because we do not put a 1 next to a base number. 2) 6 3 ÷ 6 3 = 1 Because 6 goes into 6 once, 6x6x6 (216) goes into 6x6x6 (216) once. Any number divided by itself is 1.