#8: 5 - -4·-6
#9: 12 - (-6)²
#10: 5(-7 - 15)
#11: -5 + -13 + 5 - -6
#12: (23 - 8)/(-8 + 11)
#13: 9 + 5³ - -5
#14: (13·2)/(-13)
#15: 1 - (-13 - 1 - 10)
#16: ((33 - 3)·2)/5
#17: (-25 + -5 - 2)/((-2)³)

Question

Accepted Answer

### #8:
# Explanation:
## Step1: Multiply -4 and -6
First, we handle the multiplication operation: $-4 \cdot -6 = 24$ (since the product of two negative numbers is positive).
## Step2: Subtract the result from 5
Now, we perform the subtraction: $5 - 24 = -19$ (because 5 is less than 24, the result is negative).
# Answer: $-19$

### #9:
# Explanation:
## Step1: Calculate the square of -6
First, we calculate $(-6)^2$. Squaring a negative number gives a positive result, so $(-6)^2 = 36$.
## Step2: Subtract the result from 12
Then, we do the subtraction: $12 - 36 = -24$ (since 12 is less than 36, the result is negative).
# Answer: $-24$

### #10:
# Explanation:
## Step1: Simplify the expression inside the parentheses
First, we simplify $-7 - 15$. Subtracting 15 from -7 gives $-7 - 15 = -22$ (because we are adding two negative numbers in effect: $-7 + (-15) = -22$).
## Step2: Multiply by 5
Then, we multiply this result by 5: $5 \times (-22) = -110$ (the product of a positive and a negative number is negative).
# Answer: $-110$

### #11:
# Explanation:
## Step1: Combine like terms (positive and negative integers)
First, let's rewrite the expression with proper signs: $-5 - 13 + 5 + 6$ (since $+ -13$ is $-13$ and $- -6$ is $+6$). Now, combine the positive terms: $5 + 6 = 11$, and the negative terms: $-5 - 13 = -18$.
## Step2: Add the results of the combined terms
Then, add these two results: $-18 + 11 = -7$ (because the negative term has a larger absolute value).
# Answer: $-7$

### #12:
# Explanation:
## Step1: Simplify the numerator and the denominator separately
First, simplify the numerator: $23 - 8 = 15$. Then, simplify the denominator: $-8 + 11 = 3$ (since 11 - 8 = 3 and the sign is positive because 11 has a larger absolute value).
## Step2: Divide the numerator by the denominator
Now, divide the numerator by the denominator: $\frac{15}{3} = 5$.
# Answer: $5$

### #13:
# Explanation:
## Step1: Calculate the cube of 5
First, we calculate $5^3$. $5^3 = 5 \times 5 \times 5 = 125$.
## Step2: Simplify the subtraction of a negative number
Next, $- -5$ is equivalent to $+5$ (subtracting a negative is adding the positive). So the expression becomes $9 + 125 + 5$.
## Step3: Add the numbers together
Now, add them: $9 + 125 = 134$, and $134 + 5 = 139$.
# Answer: $139$

### #14:
# Explanation:
## Step1: Simplify the numerator
First, calculate the numerator: $13 \cdot 2 = 26$.
## Step2: Divide the numerator by the denominator
Then, divide by the denominator: $\frac{26}{-13} = -2$ (the quotient of a positive and a negative number is negative).
# Answer: $-2$

### #15:
# Explanation:
## Step1: Simplify the expression inside the parentheses
First, simplify $-13 - 1 - 10$. Combine the terms: $-13 - 1 = -14$, and $-14 - 10 = -24$. So the expression inside the parentheses is $-24$.
## Step2: Subtract the result from 1
Now, we have $1 - (-24)$. Subtracting a negative is adding the positive, so $1 + 24 = 25$.
# Answer: $25$

### #16:
# Explanation:
## Step1: Simplify the numerator
First, simplify the numerator: $33 - 3 = 30$, then multiply by 2: $30 \cdot 2 = 60$.
## Step2: Divide the numerator by the denominator
Then, divide by 5: $\frac{60}{5} = 12$.
# Answer: $12$

### #17:
# Explanation:
## Step1: Simplify the numerator and the denominator separately
First, simplify the numerator: $-25 + -5 - 2 = -25 - 5 - 2 = -32$ (combining the negative terms). Then, simplify the denominator: $(-2)^3 = -8$ (since $(-2) \times (-2) \times (-2) = -8$).
## Step2: Divide the numerator by the denominator
Now, divide the numerator by the denominator: $\frac{-32}{-8} = 4$ (the quotient of two negative numbers is positive).
# Answer: $4$

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QUESTION IMAGE

Question

Explanation:

#8:

Step1: Multiply -4 and -6

Step2: Subtract the result from 5

Step1: Calculate the square of -6

Step2: Subtract the result from 12

Step1: Simplify the expression inside the parentheses

Step2: Multiply by 5

Answer:

#9: