write each as a product of powers.
1. $3 \times 3 \times 3 \times 4 \times 4 = $
2. $6 \times 6 \times 6 \times 6 \times 8 \times 8 = $
3. $2.5 \times 2.5 \times 8 \times 8 = $
4. $1.7 \times 1.7 \times 1.7 \times 1.7 \times 5 \times 5 = $
5. $9 \times 5 \times 5 \times 9 \times 9 = $
6. $4.6 \times 7 \times 7 \times 4.6 \times 7 = $
7. $10 \times 7.8 \times 7.8 \times 10 \times 2 \times 2 \times 10 \times 7.8 \times 7.8 = $
8. $6.3 \times 5 \times 5 \times 5 \times 6.3 \times 6.3 \times 13 \times 14^2 = $
9. $3 \times 3 \times 3^2 \times 4 \times 4 \times 5.5 \times 4^3 \times 5.5 = $

Question

Accepted Answer

{ "quality": "clear", "question_count": 9, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponents", "Product of Powers" ], "new_concepts": [], "current_concepts": [ "Exponents", "Product of Powers" ] } ## Group and count identical factors $$ \begin{aligned} \text{1.} \quad & 3 \times 3 \times 3 \times 4 \times 4 = 3^3 \times 4^2 \ \text{2.} \quad & 6 \times 6 \times 6 \times 6 \times 8 \times 8 = 6^4 \times 8^2 \ \text{3.} \quad & 2.5 \times 2.5 \times 8 \times 8 = 2.5^2 \times 8^2 \ \text{4.} \quad & 1.7 \times 1.7 \times 1.7 \times 1.7 \times 5 \times 5 = 1.7^4 \times 5^2 \ \text{5.} \quad & 9 \times 5 \times 5 \times 9 \times 9 = 9^3 \times 5^2 \ \text{6.} \quad & 4.6 \times 7 \times 7 \times 4.6 \times 7 = 4.6^2 \times 7^3 \end{aligned} $$ ## Combine factors with decimal and integer bases $$ \begin{aligned} \text{7.} \quad & 10 \times 7.8 \times 7.8 \times 10 \times 2 \times 2 \times 10 \times 7.8 \times 7.8 \ & = (10 \times 10 \times 10) \times (7.8 \times 7.8 \times 7.8 \times 7.8) \times (2 \times 2) \ & = 10^3 \times 7.8^4 \times 2^2 \ \text{8.} \quad & 6.3 \times 5 \times 5 \times 5 \times 6.3 \times 6.3 \times 13 \times 14^2 \ & = (6.3 \times 6.3 \times 6.3) \times (5 \times 5 \times 5) \times 13 \times 14^2 \ & = 6.3^3 \times 5^3 \times 13 \times 14^2 \end{aligned} $$ ## Simplify expressions containing existing powers $$ \begin{aligned} \text{9.} \quad & 3 \times 3 \times 3^2 \times 4 \times 4 \times 5.5 \times 4^3 \times 5.5 \ & = (3^1 \times 3^1 \times 3^2) \times (4^1 \times 4^1 \times 4^3) \times (5.5^1 \times 5.5^1) \ & = 3^{1+1+2} \times 4^{1+1+3} \times 5.5^{1+1} \ & = 3^4 \times 4^5 \times 5.5^2 \end{aligned} $$ | No. | Answer | |---|---| | 1 | $3^3 \times 4^2$ | | 2 | $6^4 \times 8^2$ | | 3 | $2.5^2 \times 8^2$ | | 4 | $1.7^4 \times 5^2$ | | 5 | $9^3 \times 5^2$ | | 6 | $4.6^2 \times 7^3$ | | 7 | $10^3 \times 7.8^4 \times 2^2$ | | 8 | $6.3^3 \times 5^3 \times 13 \times 14^2$ | | 9 | $3^4 \times 4^5 \times 5.5^2$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponents" ] }

No.	Answer
2	\(6^4 \times 8^2\)
3	\(2.5^2 \times 8^2\)
4	\(1.7^4 \times 5^2\)
5	\(9^3 \times 5^2\)
6	\(4.6^2 \times 7^3\)
7	\(10^3 \times 7.8^4 \times 2^2\)
8	\(6.3^3 \times 5^3 \times 13 \times 14^2\)
9	\(3^4 \times 4^5 \times 5.5^2\)

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Question

Explanation:

Group and count identical factors

Combine factors with decimal and integer bases

Simplify expressions containing existing powers

Answer: