Question

#2: (-13 - 2)(-10)
#3: \frac{(-2)^2}{4}
#4: \frac{(-42)(2)}{-12}
#5: \frac{30}{-4 - -9}
#6: (-13 + 1)
#7: (-10 + 5)^3
#8: 5 - -4 \cdot -6
#9: 12 - (-6)^2

Explanation:

Let's solve each problem one by one:

#2: $(-13 - 2)(-10)$

Step1: Simplify inside the first parentheses

$ -13 - 2=-15$

Step2: Multiply the results

$(-15)\times(-10) = 150$

#3: $\frac{(-2)^2}{4}$

Step1: Calculate the numerator

$(-2)^2=4$

Step2: Divide by the denominator

$\frac{4}{4}=1$

#4: $\frac{(-42)(2)}{-12}$

Step1: Calculate the numerator

$(-42)\times(2)=-84$

Step2: Divide by the denominator

$\frac{-84}{-12} = 7$

#5: $\frac{30}{-4 - (-9)}$

Step1: Simplify the denominator

$-4-(-9)=-4 + 9=5$

Step2: Divide the numerator by the denominator

$\frac{30}{5}=6$

#6: $(-13 + 1)^2$

Step1: Simplify inside the parentheses

$-13 + 1=-12$

Step2: Square the result

$(-12)^2 = 144$

#7: $(-10 + 5)^3$

Step1: Simplify inside the parentheses

$-10 + 5=-5$

Step2: Cube the result

$(-5)^3=-125$

#8: $5-4\cdot(-6)$

Step1: Perform the multiplication

$4\cdot(-6)=-24$

Step2: Perform the subtraction (remember subtracting a negative is adding)

$5-(-24)=5 + 24=29$

#9: $12-(-6)^2$

Step1: Calculate the square

$(-6)^2 = 36$

Step2: Perform the subtraction

$12-36=-24$

Answer:

s:
#2: $\boldsymbol{150}$
#3: $\boldsymbol{1}$
#4: $\boldsymbol{7}$
#5: $\boldsymbol{6}$
#6: $\boldsymbol{144}$
#7: $\boldsymbol{-125}$
#8: $\boldsymbol{29}$
#9: $\boldsymbol{-24}$