Flashcards in Exponents Deck (63):

1

## What are exponents?

### Powers, square roots and cube roots are exponential operations.

2

## What are powers?

###
Powers are repeated multiplication. So 5 to the power of 6 is 5 multiplied by itself 6 times.

5x5x5x5x5x5

3

## What are squares?

### Squares are numbers that have been multiplied by themselves. We can say that 5 squared is also 5 to the power of 2.

4

## What are cubes?

### Cubes are numbers that have been multiplied by themselves twice. We can say that 5 cubed is also 5 to the power of 3.

5

## What is square rooting?

### Square rooting is the inverse operation of squaring.

6

## What is cube rooting?

### Cube rooting is the inverse operation of cubing.

7

## What are perfect squares?

### Perfect squares are when whole numbers are multiplied by themselves. Since square rooting is the inverse operation of squaring, perfect square roots are whole numbers.

8

## What are perfect cubes?

### Perfect cubes are when whole numbers are multiplied by themselves twice. Since cube rooting is the inverse operation of cubing, perfect cube roots are whole numbers.

9

## What is 1 squared?

### 1

10

## What is 2 squared?

### 4

11

## What is 3 squared?

### 9

12

## What is 4 squared?

### 16

13

## What is 5 squared?

### 25

14

## What is 6 squared?

### 36

15

## What is 7 squared?

### 49

16

## What is 8 squared?

### 64

17

## What is 9 squared?

### 81

18

## What is 10 squared?

### 100

19

## What is 11 squared?

### 121

20

## What is 12 squared?

### 144

21

## What is 13 squared?

### 169

22

## What is the square root of 1?

### 1

23

## What is the square root of 4?

### 2

24

## What is the square root of 9?

### 3

25

## What is the square root of 16?

### 4

26

## What is the square root of 25?

### 5

27

## What is the square root of 36?

### 6

28

## What is the square root of 49?

### 7

29

## What is the square root of 64?

### 8

30

## What is the square root of 81?

### 9

31

## What is the square root of 100?

### 10

32

## What is the square root of 121?

### 11

33

## What is the square root of 144?

### 12

34

## What is the square root of 169?

### 13

35

## What is 1 cubed?

### 1

36

## What is 2 cubed?

### 8

37

## What is 3 cubed?

### 27

38

## What is 4 cubed?

### 64

39

## What is 5 cubed?

### 125

39

## What is 6 cubed?

### 216

40

## What is 10 cubed?

### 1000

41

## What is the cubed root of 1?

### 1

42

## What is the cubed root of 8?

### 2

43

## What is the cubed root of 27?

### 3

44

## What is the cubed root of 64?

### 4

45

## What is the cubed root of 125?

### 5

46

## What is the cubed root of 216?

### 6

47

## What is the cubed root of 1000?

### 10

48

## What must we do when two numbers that are being added together are covered by the same square root?

### The square root is like a bracket-we must add the two numbers first. The same applies for subtraction.

49

## What must we do when two numbers are being multiplied under the same square root?

### We can split them up and square root them separately, then multiply them together. The same applies for division.

50

## How do we cube/square/square root/cube root negatives?

### If you want to square the whole negative, you must put brackets around the number and the sign, then place the exponents outside the brackets.

51

## What happens when we square a square root or cube a cube root?

### They cancel each other out.

52

## How can we find the square root and cube root of square numbers?

### We can use prime factorisation. Write the number as a product of its prime factors. Multiply the squared numbers together to find out the square root of that number. To find a cube root, multiply the cubed numbers together to find out the cube root of that number.

53

## What happens when we raise a negative to an even power?

### We get a positive.

54

## What happens when we raise a negative to an odd power?

### We get a negative.

55

## What is scientific notation?

### It is a shortened way of writing numbers.

56

## How do we write things in scientific notation?

### Move the decimal comma to just after the first digit in the number. Then write times 10 to the power of however many places you moved the decimal comma.

57

## What happens when you multiply terms with the same base?

### When you multiply terms of the same base, you must add the exponents together.

58

## What happens when we divide numbers with the same base?

### We subtract the exponents.

59

## What happens when we raise a power to a power?

### We multiply exponents. It is important to remember to that the coefficient must also be raised to the power outside the bracket.

60

## What is any number to the power of 0?

### Any number to the power of 0 is equal to 1.

61

## What do square roots do?

### They divide any exponents by 2.

62