Questions: Use the order of operations to find the value of the following [ [-6^2+(7-9)^3-(-4)]-left[-3^2+5-2^3right] ]

Solution Steps

To solve the given expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). We will evaluate the expression inside the brackets first, then handle the exponents, followed by any multiplication or division, and finally addition and subtraction.

We start by evaluating each part of the expression:

1. \( -6^2 = 36 \)
2. \( (7 - 9)^3 = (-2)^3 = -8 \)
3. \( -(-4) = 4 \)
4. \( |-3|^2 = 3^2 = 9 \)
5. \( 5 = 5 \)
6. \( 2^3 = 8 \)

Next, we calculate the values inside the brackets:

• For the first bracket: \[ \text{Bracket 1} = 36 + (-8) + 4 = 36 - 8 + 4 = 32 \]

• For the second bracket: \[ \text{Bracket 2} = 9 + 5 - 8 = 9 + 5 - 8 = 6 \]

Now, we subtract the second bracket from the first: \[ \text{Result} = \text{Bracket 1} - \text{Bracket 2} = 32 - 6 = 26 \]

Final Answer