Powers and Roots: Master Exponents and Radicals

Question 1

Simplify the expression (3 multiplied by 4) squared.

Accepted Answer

36

Answer

12 squared

Answer

12

Answer

24

Question 2

Evaluate the expression (2 cubed) squared.

Accepted Answer

64

Answer

12

Answer

16

Answer

32

Question 3

To calculate the square of a number, what should be done?

Accepted Answer

Multiply the number by itself

Answer

Add the number to itself

Answer

Subtract the number from itself

Answer

Divide the number by 2

Question 4

What is 5 cubed?

Accepted Answer

125

Answer

15

Answer

25

Answer

625

Question 5

Calculate the value of 3 raised to the power of -2, written as 3^-2.

Accepted Answer

1/9

Answer

1/3

Answer

9

Answer

27

Question 6

Which of the following is equivalent to 2 multiplied by itself three times?

Accepted Answer

16

Answer

2

Answer

8

Answer

32

Question 7

Which expression is equivalent to the result of multiplying 3 by itself twice, and then multiplying that result by 3 again?

Accepted Answer

3^6

Answer

3^5

Answer

3^7

Answer

3^8

Question 8

Simplify the expression: (2 times x multiplied by itself three times) squared

Accepted Answer

8x^6

Answer

4x^5

Answer

4x^6

Answer

8x^5

Question 9

Which of the following is equal to the cube root of 8?

Accepted Answer

2

Answer

2^3

Answer

8^3

Answer

2/3

Question 10

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

Accepted Answer

1/9

Answer

3/2

Answer

9/3

Answer

3^2

Question 11

Simplify the expression (x^a * x^b)^c:

Accepted Answer

x^(ac + bc)

Answer

x^(a + b + c)

Answer

x^(a * b * c)

Answer

x^(a^c * b^c)

Question 12

Which of the following is a rational exponent: √(9), 1/2, π, or e^2?

Accepted Answer

1/2

Answer

√(9)

Answer

π

Answer

e^2

Question 13

What is the square of 3?

Accepted Answer

9

Answer

6

Answer

12

Answer

18

Question 14

Which of these expressions is equal to (2³)⁴?

Accepted Answer

212

Answer

27

Answer

84

Answer

164

Question 15

What is the cube root of 27?

Accepted Answer

3

Answer

9

Answer

27

Answer

81

Question 16

What is the square root of 0.25?

Accepted Answer

0.5

Answer

0.125

Answer

1.25

Answer

2.5

Question 17

Simplify the expression: 2 to the power of 5 multiplied by 2 to the power of -3

Accepted Answer

2 to the power of 2

Answer

2 to the power of 8

Answer

2 to the power of -8

Answer

2 to the power of 15

Question 18

Simplify 2^(a+b).

Accepted Answer

2^a * 2^b

Answer

2^a + 2^b

Answer

2^ab

Answer

2^(a-b)

Question 19

Simplify (2^3)^-2.

Accepted Answer

2^-5

Answer

2^-3

Answer

2^5

Answer

2^3

Question 20

Which of the following represents 5 multiplied by itself 5 times in index form?

Accepted Answer

5^5

Answer

5^2

Answer

2^5

Answer

5/2

Question 21

Which of the following is an example of a rational index?

Accepted Answer

1/2

Answer

π

Answer

√2

Answer

e

Question 22

Simplify the expression: 2^3 multiplied by 2^4.

Accepted Answer

2^7

Answer

4^7

Answer

8^7

Answer

16^7

Question 23

Which of the following is equivalent to the square root of x^8?

Accepted Answer

x^4

Answer

x^2

Answer

x^8

Answer

x^16

Question 24

What is the correct order of operations for powers and roots?

Accepted Answer

Powers, Roots, Multiplication, Division

Answer

Roots, Powers, Multiplication, Division

Answer

Multiplication, Division, Powers, Roots

Answer

Division, Multiplication, Powers, Roots

Question 25

Simplify the expression: 3√(81/27)

Accepted Answer

3

Answer

1

Answer

9

Answer

27

Question 26

Which of the following is the correct simplified form of √(125x^6)?

Accepted Answer

25x^4

Answer

5x^3

Answer

5x^4

Answer

25x^3

Question 27

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

Accepted Answer

5 + 2√(6)

Answer

1 - √(6)

Answer

1 + √(6)

Answer

5 - 2√(6)

Question 28

What is the value of 3 raised to the power of -2?

Accepted Answer

1/9

Answer

-9

Answer

-3

Answer

1/3

Question 29

Which property of powers with the same base is correct?

Accepted Answer

(a^m) * (a^n) = a^(m+n)

Answer

(a^m) * (a^n) = a^(m-n)

Answer

(a^m)^n = a^(m/n)

Answer

(a^m)^n = a^(n/m)

Question 30

Evaluate 2^-3:

Accepted Answer

1/8

Answer

2^3

Answer

1/2^3

Answer

8

Question 31

Which of the following expressions is irrational?

Accepted Answer

√2

Answer

√4

Answer

√9

Answer

√16

Question 32

Solve for x: 2 to the power of x equals 16

Accepted Answer

4

Answer

2

Answer

3

Question 33

Solve for x: x to the power of 1/2 equals 4

Accepted Answer

2

Answer

8

Answer

16

Question 34

Simplify the expression 5^2 * 5^3:

Accepted Answer

5^6

Answer

5^5

Answer

25^5

Answer

25^6

Question 35

What is the square root of 144?

Accepted Answer

6

Answer

12

Answer

8

Answer

10

Question 36

Which expression is equivalent to 3⁴?

Accepted Answer

3 × 3 × 3 × 3

Answer

3 + 3 + 3 + 3

Answer

3 × 3

Answer

3 / 3

Question 37

Find the value of 2 to the power of negative 3.

Accepted Answer

0.125

Answer

0.5

Answer

0.25

Answer

0.75

Question 38

Identify the index of 2 in the expression 2⁵.

Accepted Answer

5

Answer

2

Answer

3

Answer

10

Question 39

Simplify the expression: (x squared y cubed) to the power of negative 2

Accepted Answer

x to the power of negative 4 y to the power of negative 6

Answer

x to the power of 4 y to the power of 6

Answer

x to the power of negative 2 y to the power of negative 3

Answer

x squared y cubed

Question 40

Which of the following is an irrational number?

Accepted Answer

Pi

Answer

The square root of 4

Answer

1/2

Answer

3

Question 41

Simplify the expression: 2 to the power of 3 multiplied by 2 to the power of negative 5

Accepted Answer

2 to the power of negative 2

Answer

2 to the power of 8

Answer

2 to the power of negative 8

Answer

2 to the power of 2

Question 42

Which of the following is equivalent to 3 to the power of negative 2?

Accepted Answer

1/9

Answer

1/3 squared

Answer

3 squared

Answer

9

Question 43

Evaluate (∛125)²

Accepted Answer

25

Answer

35

Answer

45

Answer

15

Question 44

Which expression is equivalent to 3 raised to the power of -2 (3^(-2))?

Accepted Answer

1/9

Answer

9/3

Answer

3/9

Answer

9^(-2)

Question 45

Solve for x in the equation x^2 = 25.

Accepted Answer

±5

Answer

10

Answer

-5

Answer

+5

Question 46

What is the cube root of 27 (³√27)?

Accepted Answer

3

Answer

81

Answer

27

Answer

9

Question 47

Simplify the expression (4x^2y)^-1.

Accepted Answer

1/4x^2y

Answer

4x^2y

Answer

1/16x^2y