1.
Evaluate the expression when x = -5, and y = 4 (x^3 + y^2)
Correct Answer
B. -109
Explanation
The expression requires us to substitute the given values of x and y into the equation and then evaluate it. When we substitute x = -5 and y = 4 into the equation (x^3 + y^2), we get (-5^3 + 4^2). This simplifies to (-125 + 16) which equals -109. Therefore, the correct answer is -109.
2.
Which evaluation will result in a positive integer?
Correct Answer
D. (-8)^2
Explanation
The expression (-8)^2 will result in a positive integer because when a negative number is raised to an even power, the result is always positive. In this case, (-8)^2 means multiplying -8 by itself, resulting in 64, which is a positive integer.
3.
Evaluate the expression 4(-3^2)
Correct Answer
B. -36
Explanation
The expression 4(-3^2) can be simplified by first evaluating the exponent, which is -3^2. According to the order of operations, exponentiation should be done before multiplication. Squaring -3 gives us 9. Then, we multiply 4 by 9, resulting in -36. Therefore, the correct answer is -36.
4.
Evaluate the expression -3 - (-6 + 4^2)
Correct Answer
A. -13
Explanation
To evaluate the expression, we start by calculating the value inside the parentheses first. (-6 + 4^2) means we need to square 4 first, which gives us 16. Then, we add -6 to 16, resulting in 10. Now, we can substitute this value back into the expression: -3 - 10. By subtracting 10 from -3, we get -13. Therefore, the correct answer is -13.
5.
Evaluate the expression when x = - 4 and y = - 2 ----- 2x^3(-y^4)
Correct Answer
D. 2048
Explanation
When x = -4 and y = -2, we can substitute these values into the expression 2x^3(-y^4):
2(-4)^3(-(-2)^4)
Simplifying the expression inside the parentheses:
2(-64)(-16)
Multiplying the numbers:
-128(-16)
Multiplying the numbers again:
2048
Therefore, the correct answer is 2048.
6.
Which expression will result in a positive integer?
Correct Answer
B. 6(4 - 6)^2
Explanation
The expression 6(4 - 6)^2 will result in a positive integer because the base of the exponent, (4 - 6), is negative. When a negative number is squared, it becomes positive. Therefore, the result of the expression will be positive.
7.
If a is a positive integer, which best describes the evaluation of: a^2 - (-a^2)?
Correct Answer
C. The answer will be a positive integer
Explanation
When we simplify the expression a^2 - (-a^2), we can rewrite it as a^2 + a^2, which is equal to 2a^2. Since a is a positive integer, squaring it will also result in a positive integer. Therefore, when we multiply a positive integer by 2, the answer will still be a positive integer. Hence, the answer will be a positive integer.
8.
Which value makes the equation true? ___^3 = -216
Correct Answer
A. -6
Explanation
The given equation is asking for a value that, when raised to the power of 3, equals -216. The correct answer is -6 because when -6 is cubed, it equals -216.
9.
Assume b is a negative integer. Which best describes the difference of b^2 - b^2
Correct Answer
B. The difference is 0
Explanation
The difference between b^2 and b^2 is always 0, regardless of the value of b. This is because when you subtract the same value from itself, the result is always 0. Therefore, the correct answer is that the difference is 0.
10.
Evaluate the expression ((-4^2) - 8) / -2^3
Correct Answer
D. 3
Explanation
The given expression can be simplified by following the order of operations. First, we calculate the exponentiation: -4^2 equals -16 and -2^3 equals -8. Then, we perform the subtraction: -16 - 8 equals -24. Finally, we divide -24 by -8 which gives us 3. Therefore, the correct answer is 3.