Master Real Numbers and Exponents: Interactive Quizzes and Practice

Question 1

Which property ensures that the sum of any two real numbers is always a real number?

Accepted Answer

Closure property of addition

Answer

Commutative property of addition

Answer

Associative property of addition

Answer

Distributive property of multiplication over addition

Question 2

Which operation, when performed on two polynomials, does not result in a polynomial?

Accepted Answer

Dividing

Answer

Adding

Answer

Subtracting

Answer

Multiplying

Question 3

Solve for x: 2x - 11 = -17

Accepted Answer

x = -3

Answer

x = 3

Answer

x = 4

Answer

x = 7

Question 4

Which operation is **not** valid for real numbers?

Accepted Answer

Finding the derivative

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 5

Simplify the expression using the distributive property: 2(x + 3)

Accepted Answer

2x + 6

Answer

2x + 3

Answer

x + 6

Answer

x + 9

Question 6

Find the product of (2x + 3) and (x - 5).

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 + 7x - 15

Answer

2x^2 - 15x + 3

Answer

2x^2 + 15x + 3

Question 7

Identify the option that does not represent an algebraic expression:

Accepted Answer

x = 5

Answer

2x + 5

Answer

5(x - 3)

Answer

x^2 - 4

Question 8

Find the slope of the line represented by the equation y = 2x + 3.

Accepted Answer

2

Answer

1

Answer

3

Question 9

Solve for x: 3x - 5 = 10

Accepted Answer

x = 5

Answer

x = -1

Answer

x = 10

Question 10

Factor the expression x^2 - 9 into its simplest form.

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

(x + 9)(x - 1)

Answer

Cannot be factored

Question 11

Consider the equation y = 2x + 1. Which of the following options describes its graph?

Accepted Answer

A line with a slope of 2 and a y-intercept of 1

Answer

A line with a slope of 1 and a y-intercept of 2

Answer

A parabola with a vertex at (1, 2)

Question 12

Solve the inequality: 2x - 5 is less than 7

Accepted Answer

x is less than 6

Answer

x is greater than 6

Answer

x is less than -6

Answer

x is greater than -6

Question 13

Which of the following is greater: 2^4 or 4^2?

Accepted Answer

2^4

Answer

4^2

Answer

They are equal

Answer

Cannot be determined

Question 14

Simplify the expression (x^2 + 2x)(x - 3):

Accepted Answer

x^3 + x^2 - 6x

Answer

x^3 - x^2 - 6x

Answer

x^3 + 7x - 6

Answer

x^3 - 7x - 6

Question 15

Which of the following is true about the number 0.00000001?

Accepted Answer

It is a rational number

Answer

It is an irrational number

Answer

It is an integer

Answer

It is a decimal

Question 16

A radioactive substance has a half-life of 100 years. If you start with 100 grams of the substance, how many grams will remain after 200 years?

Accepted Answer

25 grams

Answer

50 grams

Answer

75 grams

Answer

100 grams

Question 17

What is the value of (2 to the power of 5) to the power of 3?

Accepted Answer

2 to the power of 15

Answer

2 to the power of 10

Answer

2 to the power of 8

Question 18

Expand the expression (a + b)^2 and simplify the result to obtain the form a^2 + 2ab + b^2.

Accepted Answer

a^2 + 2ab + b^2

Answer

a + 2ab + b

Answer

a^2 + 2b^2

Question 19

Which number is NOT included in the set of real numbers?

Accepted Answer

π

Answer

√2

Answer

-5

Answer

0.123...

Question 20

Simplify the expression: [(3a)²b⁻¹]²

Accepted Answer

9a⁴b⁻²

Answer

9a²b⁻²

Answer

3a⁴b²

Answer

3a²b²

Question 21

Find the greatest value from the given options:

Accepted Answer

√5

Answer

1.414

Answer

3/2

Answer

1.5

Question 22

Estimate the value of √27 using perfect squares.

Accepted Answer

5

Answer

4.5

Answer

5.5

Answer

6

Question 23

Simplify the expression √(48x^4) - √(27x^3) and write the answer in its simplest radical form.

Accepted Answer

6x^2 - 3x^(3/2)

Answer

12x^2 + 3x^(3/2)

Answer

6x^3 - 3x^(5/2)

Answer

12x^3 + 3x^(5/2)

Question 24

Simplify the expression: (3^2)^3

Accepted Answer

243

Answer

9

Answer

27

Answer

81

Question 25

Evaluate: √(16 + 9)

Accepted Answer

7

Answer

3

Answer

5

Answer

9

Question 26

Solve for x: 2x - 5 = 9

Accepted Answer

6

Answer

2

Answer

4

Answer

8

Question 27

Which of the following is equivalent to -2^3?

Accepted Answer

-8

Answer

-6

Answer

6

Answer

8

Question 28

Which of the following is the greatest number?

Accepted Answer

1

Answer

-0.5

Answer

0

Answer

0.5

Question 29

Which of the following is a rational number?

Accepted Answer

-3/4

Answer

√2

Answer

π

Answer

0.123456789...

Question 30

Simplify the expression: (3x^2y)^3

Accepted Answer

27x^6y^3

Answer

9x^5y^3

Answer

9x^6y^3

Answer

27x^5y^2

Question 31

Solve the equation: 2x + 5 = 15

Accepted Answer

x = 10

Answer

x = 5

Answer

x = 20

Answer

x = 25

Question 32

Find the least common multiple (LCM) of 6 and 12.

Accepted Answer

24

Answer

2

Answer

6

Answer

12

Question 33

Which of the following is an irrational number?

Accepted Answer

√2

Answer

0.25

Answer

5/7

Answer

-10

Question 34

Which of the following is a rational number?

Accepted Answer

0.1234567...

Answer

π

Answer

√3

Answer

e

Question 35

Which of the following is equivalent to 2^-3?

Accepted Answer

1/8

Answer

-2/3

Answer

1/2^3

Answer

8

Question 36

Which of the following is not considered a real number?

Accepted Answer

∞

Answer

0

Answer

√2

Answer

π

Question 37

Solve for x: 3x - 5 > 10

Accepted Answer

x > 15

Answer

x > 5

Answer

x < 5

Answer

x < 15

Question 38

Which of the following numbers is the greatest?

Accepted Answer

√3

Answer

0.5

Answer

1/3

Answer

1/4

Question 39

Solve for y: 2(y - 3) = 4 + y

Accepted Answer

y = 5

Answer

y = -5

Answer

y = 3

Answer

y = -3

Question 40

Find the value of x: 2x - 5 = 15

Accepted Answer

10

Answer

5

Answer

20

Answer

40

Question 41

Which of these is NOT a rational number?

Accepted Answer

π

Answer

0.5

Answer

-3/4

Answer

√2

Question 42

Solve for x: |x| = 5

Accepted Answer

x = 5 or x = -5

Answer

5

Answer

-5

Answer

There is no solution

Question 43

Evaluate the expression: 2^(-3)

Accepted Answer

1/8

Question 44

Simplify the expression: sqrt(16) - sqrt(4)

Accepted Answer

4

Answer

2

Question 45

Evaluate the expression: (0.5)^-2

Accepted Answer

4

Answer

0.5

Question 46

Simplify the expression: sqrt(8) * sqrt(2)

Accepted Answer

4sqrt(2)

Question 47

Simplify the expression: (3 to the power of -2 multiplied by 2 to the power of 5) divided by (2 to the power of 3 multiplied by 3 to the power of -1)

Accepted Answer

1/12

Answer

6

Answer

1/6

Answer

12

Question 48

Multiply the following monomials: 3x²y * 2xy³

Accepted Answer

6x3y4

Answer

6xy7

Answer

12x2y3

Answer

2x3y4

Question 49

Which of the given numbers is a rational number?

Accepted Answer

-3/4

Answer

π

Answer

√2

Question 50

Evaluate the numerical expression: 2^(3-1)

Accepted Answer

4

Answer

8

Answer

1

Answer

2

Question 51

Which of the following is NOT considered a real number?

Accepted Answer

√-1

Answer

1/2

Answer

π

Answer

0

Question 52

Simplify the expression: (3^2)^2

Accepted Answer

3^4

Answer

9^2

Answer

6^2

Question 53

Solve for x: 2x - 5 = 11

Accepted Answer

8

Answer

12

Answer

10

Answer

6

Question 54

Which of the following is equivalent to 10^-2?

Accepted Answer

0.01

Answer

0.1

Answer

100

Answer

10

Question 55

Which of the following is the smallest number represented on the number line?

Accepted Answer

-0.5

Answer

1

Answer

0

Answer

0.25

Question 56

Evaluate the expression: 2^3 + 3^2

Accepted Answer

17

Answer

10

Answer

13

Answer

15

Question 57

Which of the following is equivalent to writing 100,000 using exponential notation?

Accepted Answer

10^5

Answer

10^4

Answer

10^3

Answer

10^6

Question 58

Simplify the expression: (2^-2)^3

Accepted Answer

2^6

Answer

2^-3

Answer

2^2

Answer

2^-6

Question 59

Which of the following is **NOT** a property of real numbers?

Accepted Answer

Every real number has a multiplicative inverse.

Answer

The square of any real number is non-negative.

Answer

Every real number can be represented on a number line.

Answer

The sum of two real numbers is always a real number.

Question 60

Which of the following is equivalent to 5 × 10³?

Accepted Answer

5000

Answer

50

Answer

500

Answer

5

Question 61

Solve the inequality: |x - 3| > 5

Accepted Answer

x < -2 or x > 8

Answer

x > -2 or x < 8

Answer

x < 2 or x > 8

Answer

x < -8 or x > 2

Question 62

Which of the following represents the set of all rational numbers greater than 0 but less than 1?

Accepted Answer

{x | 0 < x < 1, x ∈ Q}

Answer

{x | 0 ≤ x < 1, x ∈ Q}

Answer

{x | 0 ≤ x ≤ 1, x ∈ Q}

Answer

{x | 0 < x ≤ 1, x ∈ Q}

Question 63

Which of these is NOT a real number?

Accepted Answer

√(-1)

Answer

0

Answer

π

Answer

-3.14

Question 64

What is the value of 2⁻³ + 3⁻¹?

Accepted Answer

1/6

Answer

1/12

Answer

1/3

Answer

3/4