What expression is represented by (32)4 ?

(3 x 3 x 3 x 3) (3 x 3 x 3 x 3) (3 x 3 x 3 x 3) (3 x 3 x 3 x 3)

Power And Exponent Laws

1. Write (-4) x (-4) x (-4) x (-4) x (-4) x (-4) as a power.

(-4)6

6 × (-4)

-(4)6

(-4)5

The given expression (-4) x (-4) x (-4) x (-4) x (-4) x (-4) can be simplified as (-4) raised to the power of 6. This means that the number -4 is multiplied by itself 6 times. So the correct answer is (-4)6.

Explanation

The given expression (-4) x (-4) x (-4) x (-4) x (-4) x (-4) can be simplified as (-4) raised to the power of 6. This means that the number -4 is multiplied by itself 6 times. So the correct answer is (-4)6.

2. Write (-8)⁶ ÷ (-8)³ as a single power.

(-8)2

(-8)3

(-8)9

(-8)18

To simplify the expression (-8)6 ÷ (-8)3 as a single power, we can subtract the exponents since the base is the same. Therefore, (-8)6 ÷ (-8)3 can be written as (-8)6-3, which simplifies to (-8)3.

Explanation

To simplify the expression (-8)6 ÷ (-8)3 as a single power, we can subtract the exponents since the base is the same. Therefore, (-8)6 ÷ (-8)3 can be written as (-8)6-3, which simplifies to (-8)3.

3. Express 7⁹ x 7³ ÷ 7⁶ as a single power.

72

76

718

721

not-available-via-ai

Explanation

not-available-via-ai

4. What expression is represented by (3²)⁴?

(3 x 3)(3 x 3 x 3 x 3)

(3 x 3 x 3 x 3 x 3 x 3)

(3 x 3) (3 x 3) (3 x 3) (3 x 3)

The expression (32)4 represents multiplying 3 by itself 4 times. In other words, it is equal to (3 x 3) (3 x 3) (3 x 3) (3 x 3), which simplifies to 3^4 or 81.

Explanation

The expression (32)4 represents multiplying 3 by itself 4 times. In other words, it is equal to (3 x 3) (3 x 3) (3 x 3) (3 x 3), which simplifies to 3^4 or 81.

5. Write (7³)² x (7)⁴ as a single power.

72

79

710

713

To write (73)2 x (7)4 as a single power, we can use the rule of exponents that states when multiplying powers with the same base, we add the exponents. In this case, the base is 7. So, adding the exponents 3 and 2, we get 5. Therefore, the answer is 7^10.

Explanation

To write (73)2 x (7)4 as a single power, we can use the rule of exponents that states when multiplying powers with the same base, we add the exponents. In this case, the base is 7. So, adding the exponents 3 and 2, we get 5. Therefore, the answer is 7^10.

6. Evaluate: 3³ - 4²

-11

1

7

11

The correct answer is 11 because when subtracting 42 from 33, we get a negative value of -9. However, since the question asks for the evaluation, we consider the absolute value of -9, which is 9. Therefore, the answer is 9.

Explanation

The correct answer is 11 because when subtracting 42 from 33, we get a negative value of -9. However, since the question asks for the evaluation, we consider the absolute value of -9, which is 9. Therefore, the answer is 9.

7. Write (3 x 10⁴) + (5 x 10³) + (7 x 10²) + (4 x 10¹) + (6 x 10⁰) in standard form.

35 746

3574

35 741

35 740

To write the given expression in standard form, we need to evaluate each term and add them together.

(3 x 10^4) = 30,000
(5 x 10^3) = 5,000
(7 x 10^2) = 700
(4 x 10^1) = 40
(6 x 10^0) = 6

Adding these values together, we get:
30,000 + 5,000 + 700 + 40 + 6 = 35,746

Therefore, the correct answer is 35,746.

Explanation

To write the given expression in standard form, we need to evaluate each term and add them together.

(3 x 10^4) = 30,000
(5 x 10^3) = 5,000
(7 x 10^2) = 700
(4 x 10^1) = 40
(6 x 10^0) = 6

Adding these values together, we get:
30,000 + 5,000 + 700 + 40 + 6 = 35,746

Therefore, the correct answer is 35,746.

8. Which statement is true?

(46)3 = 49

46 × 43 = 718

40 = 0

$\frac{4^6}{4^3} = 4^3$

The statement "46 × 43 = 718" is true because when we multiply 46 by 43, we get the product 1978.

Explanation

The statement "46 × 43 = 718" is true because when we multiply 46 by 43, we get the product 1978.

9. Write [(−7) x 3]⁴ as a product of powers.

4(−7) × 3

(−4)4

(−7)4 + 34

(−7)4 × 34

not-available-via-ai

Explanation

not-available-via-ai

10. Write (5 x 10⁴) + (8 x 10¹) + (9 x 10²) + (6 x 10⁰) in standard form.

50 980

50 986

50 981

5986

To express the given expression in standard form, we need to add the terms together. The first term is (5 x 10^4), which is equal to 50,000. The second term is (8 x 10^1), which is equal to 80. The third term is (9 x 10^2), which is equal to 900. The fourth term is (6 x 10^0), which is equal to 6. Adding these terms together, we get 50,000 + 80 + 900 + 6 = 50,986. Therefore, the correct answer is 50,986.

Explanation

To express the given expression in standard form, we need to add the terms together. The first term is (5 x 10^4), which is equal to 50,000. The second term is (8 x 10^1), which is equal to 80. The third term is (9 x 10^2), which is equal to 900. The fourth term is (6 x 10^0), which is equal to 6. Adding these terms together, we get 50,000 + 80 + 900 + 6 = 50,986. Therefore, the correct answer is 50,986.

11. Write as a quotient of powers: $\left (\frac{5}{3} \right )^3$

53 - 33

23

$\frac{5^3}{3^1}$

$\frac{5^3}{3^3}$

To write the given expression as a quotient of powers, we can subtract the exponents of the same base. In this case, the base is 2. The exponent of 2 in the numerator is 3, and the exponent of 2 in the denominator is 3. Subtracting these exponents gives us 3 - 3 = 0. Therefore, the expression can be written as 2^0, which simplifies to 1.

Explanation

To write the given expression as a quotient of powers, we can subtract the exponents of the same base. In this case, the base is 2. The exponent of 2 in the numerator is 3, and the exponent of 2 in the denominator is 3. Subtracting these exponents gives us 3 - 3 = 0. Therefore, the expression can be written as 2^0, which simplifies to 1.

12. Express as a single power: $\frac{(-5)^9 \times (-5)^6}{(-5)^3}$

(-5)5

(-5)51

(-5)12

(-5)18

The given expression (-5)12 represents the power of -5 raised to the exponent of 12. This means that -5 is multiplied by itself 12 times. The negative sign indicates that each multiplication will result in a negative value. Therefore, the answer (-5)12 is a negative number.

Explanation

The given expression (-5)12 represents the power of -5 raised to the exponent of 12. This means that -5 is multiplied by itself 12 times. The negative sign indicates that each multiplication will result in a negative value. Therefore, the answer (-5)12 is a negative number.

13. The solution to the following calculation is incorrect. Identify the step in which the error was made. $-\left (3.7 \right ) \times \left (2.8+-1.5 \right )-4.8 \div (-1.2)$ Step 1: $\left (-3.7 \right ) \times 1.3-4.8 \div \left (-1.2 \right )$ Step 2: $\left (-3.7 \right ) \times (-3.5) \div -1.2$ Step 3: $12.95 \div -1.2$ Step 4: $-10.7917$

Step 1

Step 2

Step 3

Step 4

not-available-via-ai

Explanation

not-available-via-ai

14. Evaluate: (7 - 2)³ + 48 ÷ (-2)⁴

338

128

10.8125

-10.8125

The expression is evaluated using the order of operations, which states that calculations inside parentheses should be done first. Therefore, (7 - 2)3 is calculated first, resulting in 5 * 3 = 15. Next, the division operation 48 ÷ (-2) is performed, resulting in -24. Finally, the addition operation 15 + (-24) is performed, resulting in -9. Therefore, the correct answer is -9, not 128.

Explanation

The expression is evaluated using the order of operations, which states that calculations inside parentheses should be done first. Therefore, (7 - 2)3 is calculated first, resulting in 5 * 3 = 15. Next, the division operation 48 ÷ (-2) is performed, resulting in -24. Finally, the addition operation 15 + (-24) is performed, resulting in -9. Therefore, the correct answer is -9, not 128.

15. Evaluate: $\left (\frac{2}{3} \right )^{3}$

$\frac{2}{27}$

$\frac{6}{9}$

$\frac{8}{27}$

$\frac{8}{9}$

not-available-via-ai

Explanation

not-available-via-ai

16. Two students were asked to write each product of powers as a single power. Their work is shown below. Danica Frank 3³ x 3² = (3 x 3 x 3) (3 x 3) 3³ x 3² = 3^{3 x 2} = 3⁵ = 3⁶ Which of the following statements about their procedures is true?

Frank’s procedure contains an error and Danica’s does not.

Danica’s procedure contains an error and Frank’s does not.

Both Danica and Frank have no errors in their procedure.

Both Danica and Frank have errors in their procedure.

Frank's procedure contains an error because he incorrectly multiplied the exponents instead of adding them. He multiplied 33 by 2 instead of adding the exponents of 3, resulting in an incorrect answer of 36. On the other hand, Danica's procedure is correct as she correctly expanded the powers and multiplied the bases, resulting in the correct answer of 35. Therefore, the statement "Frank's procedure contains an error and Danica's does not" is true.

Explanation

Frank's procedure contains an error because he incorrectly multiplied the exponents instead of adding them. He multiplied 33 by 2 instead of adding the exponents of 3, resulting in an incorrect answer of 36. On the other hand, Danica's procedure is correct as she correctly expanded the powers and multiplied the bases, resulting in the correct answer of 35. Therefore, the statement "Frank's procedure contains an error and Danica's does not" is true.

17. Which has an answer of 16?

44

-42

-32

None of the above

The correct answer is (-4)2. This is because when you square a negative number, the negative sign is removed and the result is positive. Therefore, when you square -4, you get 16.

Explanation

The correct answer is (-4)2. This is because when you square a negative number, the negative sign is removed and the result is positive. Therefore, when you square -4, you get 16.

18. Evaluate: -8⁰

8

0

1

-1

The given expression is -80 divided by 8, which equals -10. Since the number 0 is not the divisor in the expression, it is not relevant to the evaluation. Therefore, the correct answer is -10.

Explanation

The given expression is -80 divided by 8, which equals -10. Since the number 0 is not the divisor in the expression, it is not relevant to the evaluation. Therefore, the correct answer is -10.

19. Evaluate: -4² + 7⁰

-15

-9

17

23

To evaluate -42 + 70, we add the two numbers together. -42 + 70 equals 28. However, the answer given is -15, which is incorrect.

Explanation

To evaluate -42 + 70, we add the two numbers together. -42 + 70 equals 28. However, the answer given is -15, which is incorrect.

20. Which operation must be performed first in this expression? $3^2+\left [4+6\left (-8 \right ) \right ]^3$

32

4 + 6

$\left [4+6\left (-8 \right ) \right ]^3$

6(-8)

In this expression, the operation that must be performed first is the multiplication of 6 and -8, which is represented by 6(-8). This is because according to the order of operations (PEMDAS/BODMAS), multiplication should be performed before addition. Therefore, the expression should be evaluated starting with 6(-8) before moving on to the addition of 4 and 6.

Explanation

In this expression, the operation that must be performed first is the multiplication of 6 and -8, which is represented by 6(-8). This is because according to the order of operations (PEMDAS/BODMAS), multiplication should be performed before addition. Therefore, the expression should be evaluated starting with 6(-8) before moving on to the addition of 4 and 6.