Section 1.3 - Integer Operations With Powers

1. Which expression will result in a positive integer?

-4(-3 + 5)^2

6(4 - 6)^2

-7(-5 + 7)^3

5(3 - 6)^3

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.

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.

2. Which value makes the equation true? ___^3 = -216

-6

-4

4

6

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.

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.

3. Evaluate the expression when x = -5, and y = 4 (x^3 + y^2)

-141

-109

109

141

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.

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.

4. Which evaluation will result in a positive integer?

-8^2

-(-8)^2

-(8)^2

(-8)^2

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.

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.

5. Evaluate the expression -3 - (-6 + 4^2)

-13

-1

1

5

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.

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.

6. If a is a positive integer, which best describes the evaluation of: a^2 - (-a^2)?

The answer will be a negative integer

The answer will be 0

The answer will be a positive integer

The evaluation can be either postive or negative

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.

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.

7. Evaluate the expression when x = - 4 and y = - 2 ----- 2x^3(-y^4)

-2048

-256

256

2048

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.

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.

8. Evaluate the expression 4(-3^2)

-144

-36

36

144

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.

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.

9. Assume b is a negative integer. Which best describes the difference of b^2 - b^2

The difference is negative

The difference is 0

The difference is positive

The difference can be negative or positive

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.

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

-3

-1

1

3

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.

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.