Class 9 Exam > Class 9 Questions > Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10...
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Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )?
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Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )...
Simplifying the Expression
Here's how we can simplify the given expression step by step:
Step 1: Rewrite the given expression
(6 * 8^(n+1) + 16 * 2^(3n-2)) / (10 * 2^(3n+1) - 7 * 8^n)
Step 2: Use the properties of exponents to simplify
(6 * 8 * 8^n + 16 * 2^3 * 2^(3n)) / (10 * 2^3 * 2^(3n) - 7 * 8^n)
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 7 * 8^n)
Step 3: Further simplify by combining like terms
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 7 * 8^n)
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 56 * 2^n)
Step 4: Factor out common terms
8^n(48 + 128 * 2^(3n-n)) / 2^n(80 * 2^(3n-n) - 56)
8^n(48 + 128 * 2^2) / 2^n(80 * 2^2 - 56)
8^n(48 + 128 * 4) / 2^n(80 * 4 - 56)
8^n(48 + 512) / 2^n(320 - 56)
8^n(560) / 2^n(264)
Step 5: Simplify the expression
560 * 8^n / 264 * 2^n
560/264 * (8^n / 2^n)
5/3 * 4^n
Therefore, the simplified expression is 5/3 * 4^n.
Here's how we can simplify the given expression step by step:
Step 1: Rewrite the given expression
(6 * 8^(n+1) + 16 * 2^(3n-2)) / (10 * 2^(3n+1) - 7 * 8^n)
Step 2: Use the properties of exponents to simplify
(6 * 8 * 8^n + 16 * 2^3 * 2^(3n)) / (10 * 2^3 * 2^(3n) - 7 * 8^n)
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 7 * 8^n)
Step 3: Further simplify by combining like terms
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 7 * 8^n)
(48 * 8^n + 128 * 2^(3n)) / (80 * 2^(3n) - 56 * 2^n)
Step 4: Factor out common terms
8^n(48 + 128 * 2^(3n-n)) / 2^n(80 * 2^(3n-n) - 56)
8^n(48 + 128 * 2^2) / 2^n(80 * 2^2 - 56)
8^n(48 + 128 * 4) / 2^n(80 * 4 - 56)
8^n(48 + 512) / 2^n(320 - 56)
8^n(560) / 2^n(264)
Step 5: Simplify the expression
560 * 8^n / 264 * 2^n
560/264 * (8^n / 2^n)
5/3 * 4^n
Therefore, the simplified expression is 5/3 * 4^n.
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Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )?
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Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )?.
Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify: (6 〖(8)〗^(n+1)+16 〖(2)〗^(3n-2))/(10 〖(2)〗^(3n+1)- 7〖(8)〗^n )?.
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