INDICES AND POWERS

Question 1

POSITIVE POWERS

HOW IS A NUMBER TO A POWER WRITTEN?

Answer 1

A NUMBER WRITTEN AS A SUPERSCRIPT AFTER A NUMBER.

Question 2

POSITIVE POWERS

WHAT ARE THE OTHER NAMES FOR A POWER?

Answer 2

• POWER
• INDICES
• EXPONENT

Question 3

POSITIVE POWERS

WHAT IS THE NUMBER TO THE LEFT OF THE POWER CALLED?

Answer 3

BASE

Question 4

POSITIVE POWERS

HOW DOES TWO TO THE POWER OF TWO LOOK?

Answer 4

2²

Question 5

POSITIVE POWERS

WHAT DOES 2² MEAN?

Answer 5

TWO SQUARED
2 X 2

Question 6

POSITIVE POWERS

HOW DOES TWO TO THE POWER OF THREE LOOK?

Answer 6

2³

Question 7

POSITIVE POWERS

WHAT DOES 2³ MEAN?

Answer 7

TWO CUBED
2 X 2 X 2

Question 8

POSITIVE POWERS

CAN THE BASE AND THE POWER BE WRITTEN AS VARIABLES?

Answer 8

YES

Question 9

POSITIVE POWERS

CAN BOTH THE BASE AND THE POWER NUMBER BE VARIABLES?

Answer 9

YES
(y^x)

Question 10

POSITIVE POWERS

FIND THE VOLUME OF A SPHERE OF 6CM

Answer 10

• RADIUS r = DIAMETER / 2
• 6/2 = 3
• VOLUME v = 4/3 X πr³
• = 4/3 X 3.142 X 3³
• = 4 X 3.142 X 3 X 3
• = 113.04 cm³

Question 11

NEGATIVE POWERS

HOW CAN WE WORK OUT A BASE RAISED TO A NEGATIVE POWER?

Answer 11

• THE BASE MUST BE RAISED TO THE SAME POSITIVE POWER
• THE RESULT MUST THEN BE INVERTED
• THE ONLY EXCEPTION IS THAT THE BASE MUST NOT BE ZERO

Question 12

NEGATIVE POWERS

HOW CAN WE INVERT A NUMBER?

Answer 12

DIVIDE ONE BY THAT NUMBER

Question 13

NEGATIVE POWERS

HOW WOULD TWO TO THE POWER OF MINUS TWO LOOK?

Answer 13

2^-2

Question 14

NEGATIVE POWERS

WHAT IS 2^-2 EQUAL TO?

Answer 14

1/(2X2) = 1/4

Question 15

NEGATIVE POWERS

WHAT IS 2^-3 EQUAL TO?

Answer 15

1/ 2 X 2 X 2 = 1/8

Question 16

NEGATIVE POWERS

WHAT IS THE GENERAL FORMULA FOR NEGATIVE POWERS?

Answer 16

a^-m = 1/a^m
a ≠ 0

Question 17

NEGATIVE POWERS

FIND THE VALUE OF (3/2)^-3

Answer 17

• (3/2) ^-3 = (2/3)³ = 2³/3³ = 8/27
• OR
  1. (3/2)³ = 3³/ 2³ = 27/8
  2. (3/2)^-3 = 1/(3/2)³ = 1/ 27/8 = 8/27

Question 18

NEGATIVE POWERS

• THE PRESSURE P EXERTED ON THE GROUND BY A SQUARE PLATE OF SIDE x SUPPORTING A WEIGHT w IS GIVEN BY
• P = wx^-2
• FIND THE VOLUME OF P IN PASCALS WHEN
• w = 300N AND x = 10cm

Answer 18

1. x = 10cm = 0.1m
2. P = wx^-2
3. = 300 x 0.1^-2
4. = 300 / 0.1²
5. P = 30,000 Pa

Question 19

FRACTIONAL POWERS

WHAT ELSE CAN A POWER BE IF NOT A NUMBER?

Answer 19

• A FRACTION
• A DECIMAL

Question 20

FRACTIONAL POWERS

WHEN EXPRESSED AS A FRACTION WHAT DOES THE DENOMINATOR INDICATE?

Answer 20

THE ROOT OF THE NUMBER

Question 21

FRACTIONAL POWERS

WHAT DOES 4^1/2 MEAN?

Answer 21

• BASE NUMBER - 4
• POWER - 1/2
• 4 TO THE POWER OF A HALF IS EQUAL TO THE SQUARE ROOT OF 4
• 4^1/2 = 2√4 = 2

Question 22

FRACTIONAL POWERS

WHAT DOES 8^1/3 MEAN?

Answer 22

• 8 TO THE POWER OF A THIRD
• IT IS EQUAL TO THE CUBE ROOT OF 8
• 8^1/3 = 3√8 = 2

Question 23

FRACTIONAL POWERS

WHAT DOES 8^0.33 MEAN?

Answer 23

• 8 TO THE POWER OF A THIRD
• IT IS EQUAL TO THE CUBE ROOT OF 8

Question 24

FRACTIONAL POWERS

HOW ARE POWERS WRITTEN IF MADE UP OF AN INTEGER AND A FRACTIONAL PART?

Answer 24

• (8²)^1/3
• OR
• 3√8²

Question 25

# FRACTIONAL POWERS CAN POWERS THAT ARE MADE UP OF AN INTEGER AND A FRACTIONAL PART BE WRITTEN AS A MIXED NUMBER?

Answer 25

NO, NEVER

Question 26

# FRACTIONAL POWERS HOW DO YOU WORK OUT AN IMPROPER FRACTION?

Answer 26

1. EACH PART OF THE FRACTION MAY BE APPLIED TO THE BASE IN SEQUENCE 2. THE NUMBERATOR AS A POSITIVE OR NEGATIVE POWER 3. THE DENOMINATOR AS A FRACTIONAL POWER

Question 27

# FRACTIONAL POWERS WHAT DOES 8^2/3 MEAN?

Answer 27

* 8 TO THE POWER OF TWO THIRDS * IT IS EQUAL TO * (8²)^1/3 * OR * ³√8²

Question 28

# FRACTIONAL POWERS HOW WOULD YOU WORK OUT ³√8²?

Answer 28

1. THE BASE NUMBER IS SQUARED 2. 8² = 64 3. THE CUBE ROOT IS THEN TAKEN 4. ³√64 = 4

Question 29

# FRACTIONAL POWERS HOW WOULD YOU WORK OUT 8^-2/3?

Answer 29

1. INVERSE THE OPERATION 2. 8^-2/3 3. 1/8^2/3 = 1/4

Question 30

# FRACTIONAL POWERS * A NON-DIMENSIONAL CONSTANT k USED IN CONNECTION WITH RECTANGULAR WEIRS IS GIVEN BY * k = H^2/3g^1/2 / n * FIND THE VALUE OF k WHEN * H = 4.56g * g = 9.81 * n = 8.42 x 10^-6

Answer 30

1. SEE PICTURE ATTACHED

Question 31

# SPECIAL CASES WHAT IS THE RULE FOR A BASE RAISED TO THE POWER OF ZERO?

Answer 31

1. ANY BASE RAISED TO THE POWER OF ZERO IS EQUAL TO 1 2. THE BASE CAN NOT BE 0 3. a^0 = 1 4. a ≠ 0

Question 32

# SPECIAL CASES WHAT IS THE RULE FOR A BASE RAISED TO THE POWER OF 1?

Answer 32

1. ANY BASE RAISED TO THE POWER OF 1 IS EQUAL TO THE VALUE OF THE BASE 2. a¹ = a

Question 33

# POWERS IN MUTIPLICATION AND DIVISION WHAT CAN YOU DO IF MULTIPLYING TWO LIKE BASE NUMBERS WITH POWERS?

Answer 33

* THE POWERS CAN BE ADDED * ONLY IF THE BASE NUMBERS ARE THE SAME * 2³ x 2² = 2^5 * (2 x 2 x 2) x (2 x 2) * 2 x 2 x 2 x 2 x 2 * 2^5

Question 34

# POWERS IN MULTIPLICATION AND DIVISION WHAT CAN YOU DO IF DIVIDING TWO LIKE BASE NUMBERS WITH POWERS?

Answer 34

* IF THE BASES ARE THE SAME THE POWERS MAY BE SUBTRACTED * 5^7 / 5^3 = 5 x 5 x 5 x 5 x 5 x 5 x 5 / 5 x 5 x 5 * 7 - 3 = 4 * 5 x 5 x 5 x 5 * = 5^4

Question 35

# LAWS OF INDICES MULTIPLICATION

Answer 35

ADD EXPONENTS

Question 36

# LAWS OF INDICES DIVISION

Answer 36

SUBTRACT EXPONENTS

Question 37

# LAWS OF INDICES POWER OF A POWER

Answer 37

MULTIPLY EXPONENTS

Question 38

# LAWS OF INDICES POWER OF 1

Answer 38

THE TERM ITSELF

Question 39

# LAWS OF INDICES POWER OF 0

Answer 39

EQUALS 1

Question 40

# LAWS OF INDICES NEGATIVE INDICES

Answer 40

TAKE THE RECIPROCAL

Question 41

# LAWS OF INDICES FRACTIONAL INDICES

Answer 41

NUMERATOR BECOMES THE EXPONENT DENOMINATOR BECOMES THE ROOT