Use the Product Rule of Exponents to simplify the expression 2 to the power of 4 ⋅2 to the power of 2

Answer 1

To simplify the expression \(2^4 \cdot 2^2\) using the Product Rule of Exponents, you add the exponents since the bases are the same. The Product Rule states that:

\[ a^m \cdot a^n = a^{m+n} \]

Applying this to your expression:

\[ 2^4 \cdot 2^2 = 2^{4+2} = 2^6 \]

Thus, the simplified expression is \(2^6\). If you need the numerical value, \(2^6 = 64\).

Answer 2

so is the answer 64?

Answer 3

Yes, that's correct! The expression \(2^4 \cdot 2^2\) simplifies to \(2^6\), which is equal to 64. So the final answer is indeed 64.

Answer 4

well your wrong

Answer 5

I apologize if there was any confusion. However, the calculation is correct:

1. Using the Product Rule of Exponents: \[ 2^4 \cdot 2^2 = 2^{4 + 2} = 2^6 \]

2. Calculating \(2^6\): \[ 2^6 = 64 \]

So, the simplified expression is \(2^6\), and its value is 64. If there’s something specific that seems incorrect or if you meant something different, please let me know!

Answer 6

yeah actually 64 ain't the answer

Answer 7

I understand there's been some confusion, and I appreciate your patience. Let's go through it step by step once more to clarify.

The original expression is:

\[ 2^4 \cdot 2^2 \]

Using the Product Rule of Exponents, we add the exponents:

\[ 2^4 \cdot 2^2 = 2^{4 + 2} = 2^6 \]

Now, calculating \(2^6\):

\[ 2^6 = 64 \]

Thus, the result of simplifying \(2^4 \cdot 2^2\) is indeed \(2^6\), which equals 64.

If you have another interpretation or if there's a different problem you're addressing, please share that context, and I'll do my best to assist further!

Answer 8

noooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo say something else besides 64 the answer (64) is wrong

Answer 9

I apologize for any frustration my previous responses may have caused. Let's break it down clearly again without reiterating that \(2^6 = 64\).

The process of applying the Product Rule of Exponents correctly gives us:

1. Starting Expression: \(2^4 \cdot 2^2\)
2. Apply Product Rule: \[ 2^4 \cdot 2^2 = 2^{4 + 2} = 2^6 \]

At this point, we arrive at \(2^6\).

If you're looking for a different interpretation or context, please clarify. Otherwise, mathematically, \(2^4 \cdot 2^2\) simplifies to \(2^6\), and its value is conventionally acknowledged as 64. If there’s a miscommunication or different aspect you want to discuss, I’m here to help!

Answer 10

okay bill nye if 64 is the answer explain to me because it isn't it's wrong but explain in the detailed respose

Answer 11

I apologize for any misunderstanding, and I appreciate your patience. Let's revisit the simplification step by step, ensuring clarity throughout the explanation.

Given Expression

You have the expression:

\[ 2^4 \cdot 2^2 \]

Step 1: Apply the Product Rule of Exponents

The Product Rule of Exponents states that when you multiply two exponents with the same base, you can add their exponents. In mathematical notation, it is expressed as:

\[ a^m \cdot a^n = a^{m+n} \]

In your case, the base \(a\) is 2, \(m\) is 4, and \(n\) is 2. So when we apply the product rule, we add the exponents:

\[ 2^4 \cdot 2^2 = 2^{4 + 2} = 2^6 \]

Step 2: Calculate \(2^6\)

Now, we compute \(2^6\):

\[ 2^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \]

Calculating that step-by-step:

1. \(2 \cdot 2 = 4\)
2. \(4 \cdot 2 = 8\)
3. \(8 \cdot 2 = 16\)
4. \(16 \cdot 2 = 32\)
5. \(32 \cdot 2 = 64\)

Thus, \(2^6\) indeed equals 64.

Summary

With the expression \(2^4 \cdot 2^2\), we applied the Product Rule to arrive at \(2^6\), and when we computed \(2^6\), we found it to equal 64.

If you assert that the answer of 64 is incorrect for another reason or context, please clarify the perspective from which you're viewing the problem, or if there’s a specific part of the process you disagree with. Understanding the context will help me provide a more accurate explanation. Thank you for your engagement, and I’m here to assist!