evaluate each expression: (4 to the power negative 2) times ( 49 x negative 1/2)

Let's evaluate the expression step by step:

Given expression: 

\[
(4^{-2}) \times (49 \times -\frac{1}{2})
\]

### Step 1: Simplify \( 4^{-2} \)
By the properties of exponents, \( 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \).

So, \( 4^{-2} = \frac{1}{16} \).

### Step 2: Simplify \( 49 \times -\frac{1}{2} \)
\[
49 \times -\frac{1}{2} = -\frac{49}{2}
\]

### Step 3: Multiply the results from Step 1 and Step 2
Now, multiply the two results:
\[
\frac{1}{16} \times -\frac{49}{2} = -\frac{49}{32}
\]

### Final Answer:
\[
- \frac{49}{32}
\]

Would you like more details on any step or have any questions?

Here are some related questions to consider:

1. What are the properties of negative exponents?
2. How would the expression change if the exponent was positive?
3. What is the result of multiplying two negative numbers?
4. Can you express \(-\frac{49}{32}\) as a decimal?
5. How do you simplify expressions with both fractions and exponents?

**Tip:** Always apply exponent rules before multiplication when simplifying complex expressions.

evaluate each expression: (4 to the power negative 2) times (49 x negative 1/2)

Learn how to evaluate the expression (4^(-2)) × (49 × -1/2) with a detailed step-by-step solution. This problem covers key concepts like negative exponents, fraction multiplication, and properties of negative numbers. Suitable for students in Grades 8-10.

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