Question

the exponent on \\(b\\) when \\(b^3\\) is multiplied by \\(b^3\\) is

Explanation:

<pre_analysis>
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"step_cot",
"blank_filling_formatter",
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"concepts_used": [
"Product Rule of Exponents"
],
"new_concepts": [],
"current_concepts": [
"Product Rule of Exponents"
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</pre_analysis>

<reasoning>

Set up the multiplication expression

\[
b^3 \cdot b^3
\]

Apply the product rule of exponents

\[
b^3 \cdot b^3 = b^{3 + 3} = b^6
\]

Identify the exponent on the base

\[
\text{Exponent} = 6
\]
</reasoning>

<answer>
The exponent on \(b\) when \(b^3\) is multiplied by \(b^3\) is <blank>6</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Product Rule of Exponents"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
"blank_filling_formatter",
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</pre_analysis>

<reasoning>

Set up the multiplication expression

\[
b^3 \cdot b^3
\]

Apply the product rule of exponents

\[
b^3 \cdot b^3 = b^{3 + 3} = b^6
\]

Identify the exponent on the base

\[
\text{Exponent} = 6
\]
</reasoning>

<answer>
The exponent on \(b\) when \(b^3\) is multiplied by \(b^3\) is <blank>6</blank>.
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Product Rule of Exponents"
]
}
</post_analysis>