Find the numerical equivalent of 25 ⋅2−2(1 point) Responses 128 128 8 8 16 16 2

Answer 1

To solve the expression \( 25 \cdot 2^{-2} \), we start by calculating \( 2^{-2} \).

\[ 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \]

Now we can substitute this into the expression:

\[ 25 \cdot 2^{-2} = 25 \cdot \frac{1}{4} = \frac{25}{4} = 6.25 \]

Since none of the answers \( 128, 8, 16, \) or \( 2 \) are equal to \( 6.25 \), it seems I may need to reevaluate or clarify the options. Let’s work with a different perspective.

To ensure accuracy, I’ll check the understanding:

1. The expression evaluates to \( 6.25 \).
2. None of the listed options correspond to this outcome.

If there was a misunderstanding in the operations or context leading to those options, please let me know, but based on what’s provided, the result of \( 25 \cdot 2^{-2} \) is \( 6.25 \).

Answer 2

can simplify and explain

Answer 3

Sure! Let's break down the expression \( 25 \cdot 2^{-2} \) step by step and simplify it in an easy-to-understand way.

Step 1: Understand the exponent

The term \( 2^{-2} \) means "2 raised to the power of -2." When a number is raised to a negative exponent, it is equivalent to taking the reciprocal of the number raised to the corresponding positive exponent.

Using this rule: \[ 2^{-2} = \frac{1}{2^2} \]

Step 2: Calculate the positive exponent

Next, we calculate \( 2^2 \): \[ 2^2 = 2 \times 2 = 4 \] So, we substitute back into the expression for the negative exponent: \[ 2^{-2} = \frac{1}{4} \]

Step 3: Substitute back into the original expression

Now replace \( 2^{-2} \) in the expression \( 25 \cdot 2^{-2} \): \[ 25 \cdot 2^{-2} = 25 \cdot \frac{1}{4} \]

Step 4: Multiply

Now, we can multiply: \[ 25 \cdot \frac{1}{4} = \frac{25}{4} \]

Step 5: Convert to decimal (optional)

To convert the fraction \( \frac{25}{4} \) to a decimal: \[ \frac{25}{4} = 6.25 \]

Conclusion

So, the simplified numerical equivalent of \( 25 \cdot 2^{-2} \) is \( 6.25 \). In the context of your original question with given answer choices (128, 8, 16, 2), it appears that the correct answer \( 6.25 \) was not one of the options provided.

If you're looking for an appropriate choice among the options, none correspond to this result. If you need further clarifications or another approach, please let me know!

Answer 4

simplify

Answer 5

Certainly! Let's simplify the expression \( 25 \cdot 2^{-2} \) more directly.

Step-by-Step Simplification

1. Start with the expression: \[ 25 \cdot 2^{-2} \]

2. Use the negative exponent rule: \[ 2^{-2} = \frac{1}{2^2} \] So we can replace \( 2^{-2} \) with \( \frac{1}{4} \): \[ 25 \cdot 2^{-2} = 25 \cdot \frac{1}{4} \]

3. Multiply: Now, calculate \( 25 \cdot \frac{1}{4} \): \[ 25 \cdot \frac{1}{4} = \frac{25}{4} \]

4. Convert the fraction to a decimal (if needed): \[ \frac{25}{4} = 6.25 \]

Final Result

Thus, the simplified form of \( 25 \cdot 2^{-2} \) is: \[ \frac{25}{4} \quad \text{or} \quad 6.25 \]

That's the simplification! If you're looking for this in a more reduced format without changing its meaning, \( \frac{25}{4} \) is already in its simplest fractional form. Let me know if you have any more questions or need further assistance!