order the expressions by choosing $$, $

Question

order the expressions by choosing $>$, $<$, or $=$.

\
\begin{aligned}
2^4 \times 2^2 & \quad ? \quad 2^8 \\
2^2 \times 4^2 & \quad ? \quad 8^2 \\
2^4 \times 4^2 & \quad ? \quad 8^8
\end{aligned}
\

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Comparing Exponential Expressions" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Comparing Exponential Expressions" ] } ## Evaluate the first expression $$ \begin{aligned} &2^4 \times 2^2 = 2^{4+2} = 2^6\ &2^6 = 64,\quad 2^8 = 256\ &64 < 256 \implies 2^4 \times 2^2 < 2^8 \end{aligned} $$ ## Evaluate the second expression $$ \begin{aligned} &2^2 \times 4^2 = 2^2 \times (2^2)^2 = 2^2 \times 2^4 = 2^6 = 64\ &8^2 = (2^3)^2 = 2^6 = 64\ &64 = 64 \implies 2^2 \times 4^2 = 8^2 \end{aligned} $$ ## Evaluate the third expression $$ \begin{aligned} &2^4 \times 4^2 = 2^4 \times (2^2)^2 = 2^4 \times 2^4 = 2^8 = 256\ &8^8 = (2^3)^8 = 2^{24}\ &256 < 2^{24} \implies 2^4 \times 4^2 < 8^8 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $2^4 \times 2^2 \quad \square \quad 2^8$ | $<$ | | 2 | $2^2 \times 4^2 \quad \square \quad 8^2$ | $=$ | | 3 | $2^4 \times 4^2 \quad \square \quad 8^8$ | $<$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

No.	Problem	Answer
2	\(2^2 \times 4^2 \quad \square \quad 8^2\)	\(=\)
3	\(2^4 \times 4^2 \quad \square \quad 8^8\)	\(<\)

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QUESTION IMAGE

Question

Explanation:

Evaluate the first expression

Evaluate the second expression

Evaluate the third expression

Answer: