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Abi Mathematics 2015 > Exponents > Flashcards

Exponents Flashcards

1
Q

What are exponents?

A

Powers, square roots and cube roots are exponential operations.

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2
Q

What are powers?

A

Powers are repeated multiplication. So 5 to the power of 6 is 5 multiplied by itself 6 times.
5x5x5x5x5x5

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3
Q

What are squares?

A

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

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4
Q

What are cubes?

A

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

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5
Q

What is square rooting?

A

Square rooting is the inverse operation of squaring.

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6
Q

What is cube rooting?

A

Cube rooting is the inverse operation of cubing.

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7
Q

What are perfect squares?

A

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.

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8
Q

What are perfect cubes?

A

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.

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9
Q

What is 1 squared?

A

1

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10
Q

What is 2 squared?

A

4

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11
Q

What is 3 squared?

A

9

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12
Q

What is 4 squared?

A

16

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13
Q

What is 5 squared?

A

25

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14
Q

What is 6 squared?

A

36

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15
Q

What is 7 squared?

A

49

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16
Q

What is 8 squared?

A

64

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17
Q

What is 9 squared?

A

81

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18
Q

What is 10 squared?

A

100

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19
Q

What is 11 squared?

A

121

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20
Q

What is 12 squared?

A

144

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21
Q

What is 13 squared?

A

169

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22
Q

What is the square root of 1?

A

1

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23
Q

What is the square root of 4?

A

2

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24
Q

What is the square root of 9?

A

3

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25
Q

What is the square root of 16?

A

4

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26
Q

What is the square root of 25?

A

5

27
Q

What is the square root of 36?

A

6

28
Q

What is the square root of 49?

A

7

29
Q

What is the square root of 64?

A

8

30
Q

What is the square root of 81?

A

9

31
Q

What is the square root of 100?

A

10

32
Q

What is the square root of 121?

A

11

33
Q

What is the square root of 144?

A

12

34
Q

What is the square root of 169?

A

13

35
Q

What is 1 cubed?

A

1

36
Q

What is 2 cubed?

A

8

37
Q

What is 3 cubed?

A

27

38
Q

What is 4 cubed?

A

64

39
Q

What is 5 cubed?

A

125

39
Q

What is 6 cubed?

A

216

40
Q

What is 10 cubed?

A

1000

41
Q

What is the cubed root of 1?

A

1

42
Q

What is the cubed root of 8?

A

2

43
Q

What is the cubed root of 27?

A

3

44
Q

What is the cubed root of 64?

A

4

45
Q

What is the cubed root of 125?

A

5

46
Q

What is the cubed root of 216?

A

6

47
Q

What is the cubed root of 1000?

A

10

48
Q

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

A

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

49
Q

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

A

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

50
Q

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

A

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
Q

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

A

They cancel each other out.

52
Q

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

A

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
Q

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

A

We get a positive.

54
Q

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

A

We get a negative.

55
Q

What is scientific notation?

A

It is a shortened way of writing numbers.

56
Q

How do we write things in scientific notation?

A

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
Q

What happens when you multiply terms with the same base?

A

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

58
Q

What happens when we divide numbers with the same base?

A

We subtract the exponents.

59
Q

What happens when we raise a power to a power?

A

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

60
Q

What is any number to the power of 0?

A

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

61
Q

What do square roots do?

A

They divide any exponents by 2.

62
Q

What do cube roots do?

A

They divide any exponents by 3.

Abi Mathematics 2015 (25 decks)

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