Question

simplify.

\\((2x^2)^4\\)

write your answer without parentheses.

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Power of a Power Rule",
"Exponent Rules"
],
"new_concepts": [],
"current_concepts": [
"Power of a Product Rule",
"Power of a Power Rule",
"Exponent Rules"
]
}
</pre_analysis>

<reasoning>

Apply the power of a product rule

\[
(2x^2)^4 = 2^4 \cdot (x^2)^4
\]

Simplify the coefficient and variable terms

\[
2^4 = 16
\]
\[
(x^2)^4 = x^{2 \cdot 4} = x^8
\]

Combine the simplified terms

\[
16x^8
\]
</reasoning>

<answer>
Simplify.
\( (2x^2)^4 \)

Write your answer without parentheses.
<blank>\(16x^8\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponent Rules"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Power of a Power Rule",
"Exponent Rules"
],
"new_concepts": [],
"current_concepts": [
"Power of a Product Rule",
"Power of a Power Rule",
"Exponent Rules"
]
}
</pre_analysis>

<reasoning>

Apply the power of a product rule

\[
(2x^2)^4 = 2^4 \cdot (x^2)^4
\]

Simplify the coefficient and variable terms

\[
2^4 = 16
\]
\[
(x^2)^4 = x^{2 \cdot 4} = x^8
\]

Combine the simplified terms

\[
16x^8
\]
</reasoning>

<answer>
Simplify.
\( (2x^2)^4 \)

Write your answer without parentheses.
<blank>\(16x^8\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponent Rules"
]
}
</post_analysis>