Exponents and Radicals: Master the Basics with Interactive Quizzes

Question 1

Simplify the following expression: (x^2y)^3 divided by (xy^2)

Accepted Answer

x³y²

Answer

xy

Answer

x³y

Answer

x²y²

Question 2

Which of the following is equivalent to (ab)^-2?

Accepted Answer

a^-2 * b^-2

Answer

a^2 * b^2

Answer

a^-1 * b^-1

Answer

a^2 / b^2

Question 3

Rationalize the denominator: 1 / √(5)

Accepted Answer

√(5) / 5

Answer

√(5)

Answer

5 / √(5)

Answer

5

Question 4

Evaluate √(169) - 2√(25).

Accepted Answer

7

Answer

3

Answer

5

Answer

9

Question 5

Simplify the expression: (4x^2y^3)^(1/2).

Accepted Answer

2x^2y^(3/2)

Answer

2x^4y^6

Answer

4x^4y^6

Answer

8x^4y^6

Question 6

Simplify 8^(3/4).

Accepted Answer

4^6

Answer

2^6

Answer

8^6

Answer

16^6

Question 7

Simplify the expression: 2√3 + 5√3

Accepted Answer

7√3

Answer

3√3

Answer

8√3

Answer

10√3

Question 8

Find the value of √144

Accepted Answer

6

Answer

12

Answer

36

Answer

72

Question 9

Find the value of 2⁻³

Accepted Answer

1/8

Answer

-1/8

Answer

-8

Answer

8

Question 10

Express the following number in scientific notation: 0.00054

Accepted Answer

5.4 x 10⁻⁴

Answer

5.4 x 10⁻³

Answer

54 x 10⁻⁴

Answer

54 x 10⁻³

Question 11

Find the value of √(64/25)

Accepted Answer

8/5

Answer

4/5

Answer

16/5

Answer

32/5

Question 12

Which of the following is the simplified form of (x^(1/2))^(1/3)?

Accepted Answer

x^(1/6)

Answer

x^(2/3)

Answer

x^(3/2)

Answer

x^(5/6)

Question 13

What is the domain of the function f(x) = √(x-2)?

Accepted Answer

x ≥ 2

Answer

x ≤ 2

Answer

x > 2

Answer

All real numbers

Question 14

Simplify the expression: (3^2)^3

Accepted Answer

3^6

Answer

3^5

Answer

9^3

Answer

9^6

Question 15

Evaluate the expression: √(16 + 9)

Accepted Answer

5

Answer

3

Answer

25

Answer

50

Question 16

Evaluate the expression: √(144)

Accepted Answer

12

Answer

6

Answer

24

Answer

36

Question 17

Solve for x in the equation: 2^(x+1) = 16

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 18

Simplify the expression: √(x^8 * y^6)

Accepted Answer

x^4y^3

Answer

x^2y^2

Answer

xy^3

Question 19

Which expression is equivalent to √(a^5 * b^3)?

Accepted Answer

a^(5/2) * b^(3/2)

Answer

(a * b)^(5/3)

Answer

√(a^2 * b^2)

Answer

a^5 * b^3

Question 20

Simplify the expression: (2^4)^2

Accepted Answer

2^8

Answer

4

Answer

16

Answer

8

Question 21

Simplify the expression: √(16x^6)

Accepted Answer

4x^3

Answer

4x

Answer

4x^2

Answer

16x^3

Question 22

Expand and simplify the expression: (√3 + √2)^2

Accepted Answer

5 + 2√6

Answer

3 + √6

Answer

5 + √6

Answer

3 + 2√6

Question 23

Simplify the expression: √(72)

Accepted Answer

6√2

Answer

2√18

Answer

12√3

Answer

8√3

Question 24

Simplify the expression: √(x^4y^8z^12)

Accepted Answer

x^2y^4z^6

Answer

xy^4z^6

Answer

x^4y^8z^12

Answer

x^2y^2z^6

Question 25

Simplify the expression: (x^3)^2 * x^-4

Accepted Answer

x^2

Answer

x^-1

Answer

x^10

Answer

x^6

Question 26

What is the value of √(100)?

Accepted Answer

10

Answer

20

Answer

5

Answer

50

Question 27

Simplify the expression: (√(16) / √4)

Accepted Answer

2

Answer

√6

Answer

√16

Answer

4

Question 28

Which of the following expressions is equivalent to x^(1/5)?

Accepted Answer

⁵√x

Answer

√x

Answer

x√5

Answer

x^5

Question 29

Solve for x: 2^(x+1) = 16.

Accepted Answer

x = 3

Answer

x = 2

Answer

x = 1

Answer

x = 4

Question 30

Simplify the expression √(x^6 y^4).

Accepted Answer

x^3 y^2

Answer

x^3 y^4

Answer

x^2 y^3

Answer

x^6 y^2

Question 31

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

Accepted Answer

1/4

Answer

4

Answer

1/16

Answer

-4

Question 32

Simplify the expression: (2^3)^4

Accepted Answer

2^12

Answer

8^4

Answer

2^6

Answer

2^7

Question 33

Evaluate: √169

Accepted Answer

13

Answer

14

Answer

15

Answer

12

Question 34

Solve for x: 2^x = 16

Accepted Answer

4

Answer

16

Answer

8

Answer

2

Question 35

Simplify: (√2)^-4

Accepted Answer

1/8

Answer

1/4

Answer

1/2

Answer

1

Question 36

Which of the following is equivalent to 8^(1/3)?

Accepted Answer

2

Answer

4

Answer

3

Answer

5

Question 37

Rationalize the denominator: 1/√5

Accepted Answer

√5/5

Answer

√5

Answer

5/√5

Answer

5

Question 38

Evaluate: ∛27

Accepted Answer

3

Answer

5

Answer

2

Answer

4

Question 39

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

Accepted Answer

x^-4 * y^6

Answer

x^-6 * y^4

Answer

x^4 * y^-6