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12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?
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12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to...
Understanding the Expression
To solve the expression 12^4 × 9^3 × 4 ÷ 6^3 × 8^2 × 27, we need to simplify each component using their prime factorization.
Step 1: Prime Factorization
- 12 = 2^2 × 3
- 9 = 3^2
- 4 = 2^2
- 6 = 2 × 3
- 8 = 2^3
- 27 = 3^3
Step 2: Rewrite the Expression
Now, substituting these factorizations into the expression:
- 12^4 = (2^2 × 3)^4 = 2^8 × 3^4
- 9^3 = (3^2)^3 = 3^6
- 4 = 2^2
- 6^3 = (2 × 3)^3 = 2^3 × 3^3
- 8^2 = (2^3)^2 = 2^6
- 27 = 3^3
Step 3: Combine and Simplify
Now substituting back into the expression:
- Numerator: 2^8 × 3^4 × 2^2 = 2^(8+2) × 3^4 = 2^10 × 3^4
- Denominator: 2^3 × 3^3 × 2^6 = 2^(3+6) × 3^3 = 2^9 × 3^3
Step 4: Final Simplification
Now, we can simplify:
- Overall Expression = (2^10 × 3^4) ÷ (2^9 × 3^3) = 2^(10-9) × 3^(4-3) = 2^1 × 3^1 = 2 × 3 = 6
Final Result
Thus, the value of the expression 12^4 × 9^3 × 4 ÷ 6^3 × 8^2 × 27 is 6.
To solve the expression 12^4 × 9^3 × 4 ÷ 6^3 × 8^2 × 27, we need to simplify each component using their prime factorization.
Step 1: Prime Factorization
- 12 = 2^2 × 3
- 9 = 3^2
- 4 = 2^2
- 6 = 2 × 3
- 8 = 2^3
- 27 = 3^3
Step 2: Rewrite the Expression
Now, substituting these factorizations into the expression:
- 12^4 = (2^2 × 3)^4 = 2^8 × 3^4
- 9^3 = (3^2)^3 = 3^6
- 4 = 2^2
- 6^3 = (2 × 3)^3 = 2^3 × 3^3
- 8^2 = (2^3)^2 = 2^6
- 27 = 3^3
Step 3: Combine and Simplify
Now substituting back into the expression:
- Numerator: 2^8 × 3^4 × 2^2 = 2^(8+2) × 3^4 = 2^10 × 3^4
- Denominator: 2^3 × 3^3 × 2^6 = 2^(3+6) × 3^3 = 2^9 × 3^3
Step 4: Final Simplification
Now, we can simplify:
- Overall Expression = (2^10 × 3^4) ÷ (2^9 × 3^3) = 2^(10-9) × 3^(4-3) = 2^1 × 3^1 = 2 × 3 = 6
Final Result
Thus, the value of the expression 12^4 × 9^3 × 4 ÷ 6^3 × 8^2 × 27 is 6.
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12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?
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12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?.
12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 12 power 4 into 9 power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?.
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