Algebra 1: Order of Operations Activity (Quiz ID FRNEG8X) featuring two problems involving exponents and parentheses.

Let's solve each problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

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Problem 1:

$$
\frac{2 \cdot 8^2 - 2^2 \cdot 8}{2 \cdot 8}
$$

#### Step 1: Evaluate exponents
- $8^2 = 64$
- $2^2 = 4$

So the expression becomes:
$$
\frac{2 \cdot 64 - 4 \cdot 8}{2 \cdot 8}
$$

#### Step 2: Perform multiplications
- $2 \cdot 64 = 128$
- $4 \cdot 8 = 32$
- Denominator: $2 \cdot 8 = 16$

Now:
$$
\frac{128 - 32}{16} = \frac{96}{16}
$$

#### Step 3: Divide
$$
\frac{96}{16} = 6
$$

✔ Answer for Problem 1: $ \boxed{6} $

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Problem 2:

$$
6 - \left[ \frac{2 + 7}{3} - (2 \cdot 3 - 5) \right]
$$

#### Step 1: Simplify inside parentheses and brackets

Start with innermost parentheses:

- $2 \cdot 3 = 6$
- $6 - 5 = 1$

So:
$$
6 - \left[ \frac{2 + 7}{3} - 1 \right]
$$

Now simplify numerator in fraction:
- $2 + 7 = 9$

So:
$$
6 - \left[ \frac{9}{3} - 1 \right]
$$

Now divide:
- $\frac{9}{3} = 3$

So:
$$
6 - [3 - 1] = 6 - 2 = 4
$$

✔ Answer for Problem 2: $ \boxed{4} $

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✔ Final Answers:

1. $ \boxed{6} $
2. $ \boxed{4} $

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