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12 to the power 4 into 9 to the power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?
Most Upvoted Answer
12 to the power 4 into 9 to the power 3 into 4 divided by 6 to the pow...
Problem Statement
We need to simplify the expression:
12^4 * 9^3 * 4 / (6^3 * 8^2 * 27).
Step 1: Factor Each Number
- 12 = 2^2 * 3
- 9 = 3^2
- 4 = 2^2
- 6 = 2 * 3
- 8 = 2^3
- 27 = 3^3
Step 2: Substitute the Factors
Now, we can rewrite the expression using the factors we identified:
- Numerator:
12^4 = (2^2 * 3)^4 = 2^8 * 3^4
9^3 = (3^2)^3 = 3^6
4 = 2^2
- Denominator:
6^3 = (2 * 3)^3 = 2^3 * 3^3
8^2 = (2^3)^2 = 2^6
27 = 3^3
Step 3: Combine the Factors
- Numerator becomes:
2^8 * 3^4 * 2^2 = 2^(8+2) * 3^4 = 2^10 * 3^4
- Denominator becomes:
2^3 * 3^3 * 2^6 = 2^(3+6) * 3^3 = 2^9 * 3^3
Step 4: Simplify the Expression
Now, substitute back into the fraction:
(2^10 * 3^4) / (2^9 * 3^3)
- For base 2:
2^(10-9) = 2^1 = 2
- For base 3:
3^(4-3) = 3^1 = 3
Final Result
Thus, the final result of the expression is:
2 * 3 = 6.
We need to simplify the expression:
12^4 * 9^3 * 4 / (6^3 * 8^2 * 27).
Step 1: Factor Each Number
- 12 = 2^2 * 3
- 9 = 3^2
- 4 = 2^2
- 6 = 2 * 3
- 8 = 2^3
- 27 = 3^3
Step 2: Substitute the Factors
Now, we can rewrite the expression using the factors we identified:
- Numerator:
12^4 = (2^2 * 3)^4 = 2^8 * 3^4
9^3 = (3^2)^3 = 3^6
4 = 2^2
- Denominator:
6^3 = (2 * 3)^3 = 2^3 * 3^3
8^2 = (2^3)^2 = 2^6
27 = 3^3
Step 3: Combine the Factors
- Numerator becomes:
2^8 * 3^4 * 2^2 = 2^(8+2) * 3^4 = 2^10 * 3^4
- Denominator becomes:
2^3 * 3^3 * 2^6 = 2^(3+6) * 3^3 = 2^9 * 3^3
Step 4: Simplify the Expression
Now, substitute back into the fraction:
(2^10 * 3^4) / (2^9 * 3^3)
- For base 2:
2^(10-9) = 2^1 = 2
- For base 3:
3^(4-3) = 3^1 = 3
Final Result
Thus, the final result of the expression is:
2 * 3 = 6.
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12 to the power 4 into 9 to the power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?
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12 to the power 4 into 9 to the 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 to the power 4 into 9 to the 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 to the power 4 into 9 to the power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?.
12 to the power 4 into 9 to the 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 to the power 4 into 9 to the 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 to the power 4 into 9 to the power 3 into 4 divided by 6 to the power 3 into 8 to the power 2 into 27?.
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