1.
Write (-8)^{6} ÷ ^{ }(-8)^{3} as a single power.
Correct Answer
B. (-8)^{3}
Explanation
To simplify the expression (-8)6 รท (-8)3 as a single power, we can subtract the exponents since the base is the same. Therefore, (-8)6 รท (-8)3 can be written as (-8)6-3, which simplifies to (-8)3.
2.
Write (7^{3})^{2} x (7)^{4} as a single power.
Correct Answer
C. 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.
3.
Evaluate: 3^{3} - 4^{2}
Correct Answer
D. 11
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.
4.
Evaluate: -4^{2} + 7^{0}
Correct Answer
A. -15
Explanation
To evaluate -42 + 70, we add the two numbers together. -42 + 70 equals 28. However, the answer given is -15, which is incorrect.
5.
Which has an answer of 16?
Correct Answer
C. -3^{2}
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.
6.
Evaluate:
Correct Answer
C.
7.
Which statement is true?
Correct Answer
D.
Explanation
The statement "46 × 43 = 718" is true because when we multiply 46 by 43, we get the product 1978.
8.
Write (3 x 10^{4}) + (5 x 10^{3}) + (7 x 10^{2}) + (4 x 10^{1}) + (6 x 10^{0}) in standard form.
Correct Answer
A. 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.
9.
Write (5 x 10^{4}) + (8 x 10^{1}) + (9 x 10^{2}) + (6 x 10^{0}) in standard form.
Correct Answer
B. 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.
10.
Write [(−7) x 3]^{4} as a product of powers.
Correct Answer
D. (−7)^{4} × 3^{4}
11.
Write (-4) x (-4) x (-4) x (-4) x (-4) x (-4) as a power.
Correct Answer
A. (-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.
12.
Express as a single power:
Correct Answer
C. (-5)^{12}
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.
Evaluate: -8^{0}
Correct Answer
D. -1
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.
14.
Write as a quotient of powers:
Correct Answer
D.
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.
15.
Express 7^{9} x 7^{3} ÷ 7^{6} as a single power.
Correct Answer
B. 7^{6}
16.
What expression is represented by (3^{2})^{4 }?
Correct Answer
C. (3 x 3) (3 x 3) (3 x 3) (3 x 3)
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.
17.
Evaluate: (7 - 2)^{3} + 48 ÷ (-2)^{4}
Correct Answer
B. 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 รท (-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.
18.
Two students were asked to write each product of powers as a single power. Their work is shown below.
Danica Frank
3^{3} x 3^{2} = (3 x 3 x 3) (3 x 3) 3^{3} x 3^{2} = 3^{3 x 2}
= 3^{5} = 3^{6}
Which of the following statements about their procedures is true?
Correct Answer
A. Frank’s procedure contains an error and Danica’s does not.
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.
19.
The solution to the following calculation is incorrect.
Identify the step in which the error was made.
Step 1:
Step 2:
Step 3:
Step 4:
Correct Answer
B. Step 2
20.
Which operation must be performed first in this expression?
Correct Answer
D. 6(-8)
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.