Chapter 2: Exponents

Question 1

What is (a^n) called?

Answer 1

Power

Question 2

What is (a) in (a^n)?

Answer 2

Base

Question 3

What is (n) in (a^n)?

Answer 3

Exponent

Question 4

What does the exponent tell you in (a^n)?

Answer 4

How many times the base is multiplied

Question 5

What is the process of writing a base with an exponent called?

Answer 5

Exponentiation

Question 6

What are the rules for calculating with powers called?

Answer 6

Exponent laws

Question 7

What is (a^n \cdot a^m)?

Answer 7

(a^{n+m})

Question 8

What is (a^n \cdot b^n)?

Answer 8

((ab)^n)

Question 9

What is (a^n / a^m)?

Answer 9

(a^{n-m})

Question 10

What is (a^n / b^n)?

Answer 10

((a/b)^n)

Question 11

What is ((a^n)^m)?

Answer 11

(a^{nm})

Question 12

What is ((1/a)^n)?

Answer 12

(1/a^n)

Question 13

What is the sign of ((-a)^n) if (n) is even?

Answer 13

Positive

Question 14

What is the sign of ((-a)^n) if (n) is odd?

Answer 14

Negative

Question 15

What is the product of a number with itself called?

Answer 15

Square

Question 16

How do you write the square of a number?

Answer 16

(a^2 = a \cdot a)

Question 17

What exponent is used for a square?

Answer 17

2

Question 18

What is the square of an integer called?

Answer 18

Perfect square

Question 19

What is ((-a)^2) equal to?

Answer 19

(a^2)

Question 20

What is always true about the sign of a square?

Answer 20

It is nonnegative

Question 21

What is ((ab)^2)?

Answer 21

(a^2b^2)

Question 22

What is ((1/a)^2)?

Answer 22

(1/a^2)

Question 23

What is ((a/b)^2)?

Answer 23

(a^2 / b^2)

Question 24

What is ((a + b)^2)?

Answer 24

(a^2 + 2ab + b^2)

Question 25

What is a number raised to the 3rd power called?

Answer 25

Cube

Question 26

What is the cube of an integer called?

Answer 26

Perfect cube

Question 27

What is the entire expression \(a^n\) called?

Answer 27

Power

Question 28

How is any number \(a\) raised to the power of 1 defined?

Answer 28

\(a^1 = a\)

Question 29

How do you simplify the power of a product \((ab)^n\)?

Answer 29

\((ab)^n = a^n b^n\)

Question 30

How do you simplify the power of a reciprocal \((1/a)^n\)?

Answer 30

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

Question 31

How do you simplify the power of a quotient \((a/b)^n\)?

Answer 31

\((a/b)^n = a^n / b^n\)

Question 32

How do you calculate the cube of a negation \((-a)^3\)?

Answer 32

\((-a)^3 = -a^3\)

Question 33

If \(n\) is an even integer, what is \((-a)^n\)?

Answer 33

\((-a)^n = a^n\)

Question 34

If \(n\) is an odd integer, what is \((-a)^n\)?

Answer 34

\((-a)^n = -a^n\)

Question 35

Is exponentiation commutative or associative?

Answer 35

Exponentiation is neither commutative nor associative

Question 36

How do you multiply powers with the same base \(a^n \cdot a^m\)?

Answer 36

\(a^{n+m}\)

Question 37

How do you divide powers with the same base \(a^n / a^m\)?

Answer 37

\(a^{n-m}\)

Question 38

How do you raise a power to another exponent \((a^n)^m\)?

Answer 38

\(a^{nm}\)

Question 39

What is any nonzero number \(a\) raised to the power of zero?

Answer 39

\(a^0 = 1\)

Question 40

How is a number \(a\) raised to a negative exponent \(-n\) defined?

Answer 40

\(a^{-n} = 1/a^n\)

Question 41

Does the rule for multiplying powers with the same base hold if the exponents are negative?

Answer 41

Yes, \(a^n \cdot a^m = a^{n+m}\)

Question 42

How do you simplify a reciprocal raised to a negative exponent \((1/a)^{-n}\)?

Answer 42

\((1/a)^{-n} = a^n\)