Exponents and Roots Quiz

Answer explanation

To simplify the expression \(3^2 \times 3^3\), use the property of exponents that states \(a^m \times a^n = a^{m+n}\). Thus, \(3^2 \times 3^3 = 3^{2+3} = 3^5\). The correct answer is \(3^5\).

What is the square root of 64?

• 6

• 7

• 8

• 9

Answer explanation

The square root of 64 is the number that, when multiplied by itself, equals 64. Since 8 x 8 = 64, the correct answer is 8.

• 14

• 20

• 18

• 12

Answer explanation

To evaluate the expression, follow the order of operations: first, multiply 3 by 4 to get 12, then add 2. Thus, 2 + 12 equals 14, which is the correct answer.

• 11

• 10

• 9

• 8

Answer explanation

To evaluate the expression 2x + 5 with x = 3, substitute 3 for x: 2(3) + 5 = 6 + 5 = 11. Therefore, the correct answer is 11.

• 5

• 6

• 7

• 8

Answer explanation

To solve for x in the equation x^2 = 49, take the square root of both sides. This gives x = ±7. Since 7 is one of the answer choices, the correct answer is 7.

Answer explanation

To simplify (2^3)^2, use the power of a power rule: (a^m)^n = a^(m*n). Here, 2^(3*2) = 2^6. However, we need to calculate 2^3 first, which is 8, and then square it: 8^2 = 64, which is 2^8.

What is the square root of 121?

• 10

• 11

• 12

• 13

Answer explanation

The square root of 121 is the number that, when multiplied by itself, equals 121. Since 11 x 11 = 121, the correct answer is 11.

• 19

• 21

• 23

• 25

Answer explanation

First, evaluate the expression inside the parentheses: 3 + 4 = 7. Then, multiply by 2: 2 × 7 = 14. Finally, add 5: 5 + 14 = 19. Thus, the correct answer is 19.

• 10

• 11

• 12

• 13

Answer explanation

To evaluate the expression 3y - 2, substitute y = 4: 3(4) - 2 = 12 - 2 = 10. Thus, the correct answer is 10.

• 2

• 3

• 4

• 5

Answer explanation

To solve for x in the equation x^3 = 27, take the cube root of both sides. The cube root of 27 is 3, so x = 3. Therefore, the correct answer is 3.