Exponents and Roots: Master the Basics with Interactive Quizzes

Question 1

Evaluate: (√2 + √3)(√2 - √3)

Accepted Answer

-1

Answer

1

Answer

-2

Answer

2

Question 2

Simplify the expression: (2³)^(1/2)

Accepted Answer

2^(3/2)

Answer

2^6

Answer

2

Answer

1/8

Question 3

Which expression is equivalent to √(16/25)?

Accepted Answer

4/5

Answer

8/5

Answer

16/25

Answer

2/5

Question 4

Solve the radical equation: √(x + 5) = 3

Accepted Answer

x = 14

Answer

x = 4

Answer

x = 5

Answer

x = -2

Question 5

Simplify the expression: 2^(-2) × (2^3 / 2^5)

Accepted Answer

1/32

Answer

1/8

Answer

32

Answer

8

Question 6

Solve the radical equation: (x - 2)^(1/2) = 5

Accepted Answer

x = 47

Answer

x = 27

Answer

x = -23

Answer

x = 2

Question 7

Simplify the expression (2^3 / 2^(-1))^(1/2).

Accepted Answer

2^2

Answer

2^1

Answer

2^3

Answer

2^4

Question 8

Find the conjugate of the expression √5 - 3.

Accepted Answer

√5 + 3

Answer

√5 - 3

Answer

-√5 + 3

Answer

-√5 - 3

Question 9

Simplify the radical expression: √(80)

Accepted Answer

4sqrt(5)

Answer

8sqrt(5)

Answer

2sqrt(20)

Answer

4sqrt(20)

Question 10

Solve the radical equation: √(x + 5) = 3

Accepted Answer

x = 4

Answer

x = -4

Answer

x = 8

Answer

x = -8

Question 11

Which of the following is equivalent to 2^(3x-5)?

Accepted Answer

8x-5

Answer

32x-5

Answer

8x/5

Question 12

Find the value of x: (x^2 - 4)^2 = 0

Accepted Answer

x = ±2

Answer

x = 2

Answer

x = 4

Question 13

Solve the radical equation: √(x - 5) = 3

Accepted Answer

x = 14

Answer

x = 4

Answer

x = 25

Answer

x = 10

Question 14

Which of the following is equivalent to the expression: √(125x⁶y⁴)

Accepted Answer

25x³y²

Answer

5x²y²

Answer

5x³y²

Answer

25x²y²

Question 15

Find the value of y such that the expression: (x²y^(1/3) - 2x) / (x^(1/2)y^(2/3) - 2) is undefined

Accepted Answer

y = 0

Answer

y = 2

Answer

y = 4

Answer

y = 8

Question 16

Simplify the expression: (2^3)^2

Accepted Answer

2^6

Answer

2^3

Answer

2^5

Answer

2^9

Question 17

Express the following expression in exponential form: ∛(x^9)

Accepted Answer

x^27

Answer

x^3

Answer

x^6

Answer

x^9

Question 18

Solve for x: √(x) = 5

Accepted Answer

x = 25

Answer

x = 2

Answer

x = 5

Answer

x = 50

Question 19

Which of the following is the reciprocal of ∛(4)?

Accepted Answer

∛(1/4)

Answer

∛(4)

Answer

4^(3/2)

Answer

4^(-3/2)

Question 20

Find the equivalent of 5^-2

Accepted Answer

1/5^2

Answer

-5^2

Answer

5^2

Answer

2/5

Question 21

Divide (x^4y^2) by (xy^3):

Accepted Answer

x^3y^-1

Answer

xy

Answer

x^3y

Answer

x^2y^-1

Question 22

Which of the following is the conjugate of √2 + 3?

Accepted Answer

√2 - 3

Answer

√2 + 3

Answer

-√2 + 3

Answer

-√2 - 3

Question 23

Simplify the expression √(x^4y^6).

Accepted Answer

x^2y^3

Answer

x^2y^6

Answer

x^4y^3

Answer

x^4y^6

Question 24

Which of the following is equivalent to 2^5 * 2^3?

Accepted Answer

2^10

Answer

2^2

Answer

2^8

Answer

2^15

Question 25

Evaluate: 3√8 + 2√50

Accepted Answer

7 + 10√2

Answer

2 + 10√2

Answer

7 + 5√2

Answer

2 + 5√2

Question 26

Which of the following is equivalent to 1/√3?

Accepted Answer

√3/3

Answer

√3

Answer

3/√3

Answer

3√3

Question 27

Express 0.0001 in scientific notation

Accepted Answer

1 x 10^-4

Answer

10 x 10^-4

Answer

100 x 10^-4

Answer

1000 x 10^-4

Question 28

Simplify: (x^2y^3)^-2

Accepted Answer

x^-4y^-6

Answer

x^4y^6

Answer

x^6y^4

Answer

x^-6y^4

Question 29

Which of the following expressions is equivalent to (2^3)^2?

Accepted Answer

16^2

Answer

6^2

Answer

8^2

Answer

32^2

Question 30

Simplify the radical expression: √(36x^2y^4)

Accepted Answer

6xy^2

Answer

6|x|y^2

Answer

|6x|y^2

Answer

6|xy^2|

Question 31

Evaluate: (2^(1/2))^(1/3)

Accepted Answer

2^(1/6)

Answer

2^(2/3)

Answer

2^(1/2)

Answer

2^(3/2)

Question 32

Simplify: (3^2/5 * 3^6/5) / 3^(2/5)

Accepted Answer

3^(12/5)

Answer

3^2

Answer

3^6

Answer

3^(6/5)

Question 33

Simplify the expression: (x^3 * x^5) / x^2

Accepted Answer

x^6

Answer

x^1

Answer

x^10

Answer

x^8

Question 34

Simplify the expression: (x^3 * x^5) / x^2

Accepted Answer

x^6

Answer

x^8

Answer

x

Answer

x^10

Question 35

What is the value of 8^(2/3)?

Accepted Answer

4

Answer

2

Answer

16

Answer

64

Question 36

Simplify the expression: √(27x^6)

Accepted Answer

3x^3√3

Answer

9x^3√3

Answer

3x^2√3

Answer

√(27x^6)

Question 37

Solve for x: √(x+5) = 3

Accepted Answer

x = 4

Answer

x = -14

Answer

x = 14

Answer

x = -4

Question 38

Simplify the expression: (√2 + √8)^2

Accepted Answer

18

Answer

12

Answer

20

Answer

10

Question 39

Which of the following is equivalent to 1/x^(-3)?

Accepted Answer

x^3

Answer

x^(-3)

Answer

-x^3

Answer

1/x^3

Question 40

What is the value of (27)^(1/3) * (16)^(1/4)?

Accepted Answer

12

Answer

24

Answer

36

Answer

6

Question 41

Simplify the expression: (√5 + √2)(√5 - √2)

Accepted Answer

3

Answer

√3

Answer

7

Answer

√7

Question 42

Solve for x: ∛(2x - 1) = 3

Accepted Answer

x = 14

Answer

x = 28

Answer

x = 7

Answer

x = 13

Question 43

Express 0.000045 in scientific notation.

Accepted Answer

4.5 x 10^(-5)

Answer

45 x 10^(-6)

Answer

4.5 x 10^(-4)

Answer

4.5 x 10^(5)