Index Laws

Question 1

What is the definition of an index?

Answer 1

An index is a shorthand notation that indicates the power to which a number (the base) is raised.

e.g. 2^4 (2 to the power of 4), 2 is the base and 4 is the index

Question 2

True or False: The index law states that a^m * a^n = a^(m+n).

Answer 2

True

Question 3

Fill in the blank: a^0 = _____ for any non-zero a.

Answer 3

1

Question 4

What is the result of a^m / a^n?

Answer 4

a^(m-n)

Question 5

If a^3 = 27, what is the value of a?

Answer 5

3

Question 6

True or False: (a^m)^n = a^(mn).

Answer 6

True

Question 7

What is the index law for multiplying powers with different bases?

Answer 7

You can only add the exponents if the bases are the same.

Question 8

If c^4 x c^2 = c^n, what is the value of n?

Answer 8

6

Question 9

Fill in the blank: (xy)^n = _____

Answer 9

x^n * y^n

Question 10

What does a negative exponent signify?

Answer 10

a^(-n) = 1/a^n

Question 11

If 3^x = 81, what is the value of x?

Answer 11

4

Question 12

True or False: a^m * b^m = (ab)^m.

Answer 12

True

Question 13

What is the value of 2^3 * 2^2?

Answer 13

32

Question 14

If a = 5 and b = 2, what is the value of 2a^2 + 3b?

Answer 14

53

Question 15

What is the result of (x^2y^3)^2?

Answer 15

x^4y^6

Question 16

Fill in the blank: a^m / a^m = _____

Answer 16

1

Question 17

What is the coefficient in the expression 4x^3?

Answer 17

4

Question 18

If (2^3)(2^4) = 2^n, what is n?

Answer 18

7

Question 19

True or False: The product of two powers with the same base is the sum of their exponents.

Answer 19

True

Question 20

What does the expression (2x^2)^3 equal?

Answer 20

8x^6

Question 21

If a = 10, what is the value of a^2?

Answer 21

100

Question 22

Fill in the blank: a^m * a^n = _____

Answer 22

a^(m+n)

Question 23

What is the value of 5^0?

Answer 23

1

Question 24

If 4^x = 64, what is x?

Answer 24

3

Question 25

True or False: (ab)^m = a^m + b^m.

Answer 25

False

Question 26

If x = 2, what is the value of 3x^2 + 5?

Answer 26

17

Question 27

What is the result of 7^3?

Answer 27

343

Question 28

If a^3b^2 = 12 and a = 2, what is b?

Answer 28

3

Question 29

Fill in the blank: a^(-m) = _____

Answer 29

1/a^m

Question 30

What is the value of (3^2)^3?

Answer 30

729

Question 31

If 2^x = 16, what is x?

Answer 31

4

Question 32

True or False: The exponent in a power indicates how many times to multiply the base.

Answer 32

True

Question 33

What is the result of x^5 / x^2?

Answer 33

x^3

Question 34

Fill in the blank: The coefficient of 7x^4 is _____

Answer 34

7

Question 35

If 10^2 = n, what is n?

Answer 35

100

Question 36

What is the result of 6^2 * 6^3?

Answer 36

7776

Question 37

If a = 3 and b = 4, what is the value of 2a^2b?

Answer 37

72

Question 38

True or False: The base of a power can be any real number.

Answer 38

True

Question 39

What is the value of (x^3)^2?

Answer 39

x^6

Question 40

If a^2 = 25, what is the value of a?

Answer 40

5 or -5