question 1 simplify: \$(x^3)^5\$ \$x^2\$ \$x^8\$ \$x^{15}\$ \\(…

QUESTION IMAGE

$question 1 simplify: \$(x^3)^5\$ \$x^2\$ \$x^8\$ \$x^{15}\$ \\(…$

Question

question 1

simplify:
\$(x^3)^5\$

\$x^2\$
\$x^8\$
\$x^{15}\$
\$x^{243}\$

question 2

simplify:
\$(y^5)^{-2}\$

\$y^{10}\$
\$-\frac{1}{y^{10}}\$
\$y^3\$
\$\frac{1}{y^{10}}\$

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Exponent Rules",
"Negative Exponents"
],
"new_concepts": [],
"current_concepts": [
"Exponent Rules",
"Negative Exponents"
]
}
</pre_analysis>

Simplify Question 1

\[
(x^3)^5 = x^{3 \times 5} = x^{15}
\]

Simplify Question 2

\[
(y^5)^{-2} = y^{5 \times (-2)} = y^{-10} = \frac{1}{y^{10}}
\]
</reasoning>

Question 1

<mcq-option>(A) $x^2$</mcq-option>
<mcq-option>(B) $x^8$</mcq-option>
<mcq-correct>(C) $x^{15}$</mcq-correct>
<mcq-option>(D) $x^{243}$</mcq-option>

Question 2

<mcq-option>(A) $y^{10}$</mcq-option>
<mcq-correct>(B) $\frac{1}{y^{10}}$</mcq-correct>
<mcq-option>(C) $y^3$</mcq-option>
<mcq-option>(D) $\frac{1}{y^3}$</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Exponent Rules"
]
}
</post_analysis>

Answer: