Final answer:
To evaluate the expressions, follow the order of operations. The evaluations are: A) 13, B) 31, C) -65, D) 6, E) -54, F) -4, G) -30, H) -18.
Step-by-step explanation:
To evaluate the given expressions, we need to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
A) (-5)^2 - 2 * (-9) + 6
Start with the exponent: (-5)^2 = 25
Next, perform the multiplication: 2 * (-9) = -18
Finally, add all the results together: 25 - 18 + 6 = 13
B) (-9) - (-8) + 2 * 4^2
First, simplify the double negative: (-9) - (-8) = -9 + 8 = -1
Next, perform the exponent: 4^2 = 16
Then, perform the multiplication: 2 * 16 = 32
Finally, add all the results together: -1 + 32 = 31
C) 8 / (-4) * (-6)^2 + 7
Start with the exponent: (-6)^2 = 36
Next, perform the division: 8 / (-4) = -2
Then, perform the multiplication: -2 * 36 = -72
Finally, add all the results together: -72 + 7 = -65
D) 10 * 5 - (-6)^2 + (-8)
Start with the exponent: (-6)^2 = 36
Next, perform the multiplication: 10 * 5 = 50
Then, perform the negation: -36 (since there's a negative sign in front of it)
Finally, add all the results together: 50 + (-36) + (-8) = 6
E) (10 / (-5) - (-2)) * (-3)^3
First, simplify the division: 10 / (-5) = -2
Next, simplify the negation: -(-2) = 2
Then, perform the exponent: (-3)^3 = -27
Finally, perform the multiplication: 2 * (-27) = -54
F) 3 * 10 + 8 - 42
Perform the multiplication: 3 * 10 = 30
Then, perform the addition: 30 + 8 = 38
Finally, perform the subtraction: 38 - 42 = -4
G) (-3)^3 - 2 + 8 / (-8)
Start with the exponent: (-3)^3 = -27
Next, perform the division: 8 / (-8) = -1
Finally, add all the results together: -27 - 2 + (-1) = -30
H) 4 * (-8) + 6 - (-2)^3
Start with the exponent: (-2)^3 = -8
Next, perform the multiplication: 4 * (-8) = -32
Then, simplify the double negative: -(-8) = 8
Finally, add all the results together: -32 + 6 + 8 = -18
Overall, the evaluations are:
A) 13
B) 31
C) -65
D) 6
E) -54
F) -4
G) -30
H) -18