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Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.?
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Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 ...
Understanding the Expression
To simplify the expression
15^(-1/5) * 225^(4/5) * 625^(-2/5) / 125^(3/5),
we will break it down step by step.
Step 1: Rewrite the Bases
- 15 = 3 * 5
- 225 = 15^2 = (3 * 5)^2 = 3^2 * 5^2
- 625 = 5^4
- 125 = 5^3
Step 2: Apply the Exponents
Now, let's apply the exponents to each base:
- 15^(-1/5) = (3 * 5)^(-1/5) = 3^(-1/5) * 5^(-1/5)
- 225^(4/5) = (3^2 * 5^2)^(4/5) = 3^(2 * 4/5) * 5^(2 * 4/5) = 3^(8/5) * 5^(8/5)
- 625^(-2/5) = (5^4)^(-2/5) = 5^(4 * -2/5) = 5^(-8/5)
- 125^(3/5) = (5^3)^(3/5) = 5^(3 * 3/5) = 5^(9/5)
Step 3: Combine the Terms
Now, substituting these back into the expression gives:
(3^(-1/5) * 5^(-1/5)) * (3^(8/5) * 5^(8/5)) * (5^(-8/5)) / (5^(9/5))
Combine like bases:
- For base 3: 3^(-1/5 + 8/5) = 3^(7/5)
- For base 5: 5^(-1/5 + 8/5 - 8/5 - 9/5) = 5^(-10/5) = 5^(-2)
Final Result
Thus, the simplified expression is:
3^(7/5) / 5^(2).
This can be further expressed as 3^(7/5) * 5^(-2) or 3^(7/5) / 25.
To simplify the expression
15^(-1/5) * 225^(4/5) * 625^(-2/5) / 125^(3/5),
we will break it down step by step.
Step 1: Rewrite the Bases
- 15 = 3 * 5
- 225 = 15^2 = (3 * 5)^2 = 3^2 * 5^2
- 625 = 5^4
- 125 = 5^3
Step 2: Apply the Exponents
Now, let's apply the exponents to each base:
- 15^(-1/5) = (3 * 5)^(-1/5) = 3^(-1/5) * 5^(-1/5)
- 225^(4/5) = (3^2 * 5^2)^(4/5) = 3^(2 * 4/5) * 5^(2 * 4/5) = 3^(8/5) * 5^(8/5)
- 625^(-2/5) = (5^4)^(-2/5) = 5^(4 * -2/5) = 5^(-8/5)
- 125^(3/5) = (5^3)^(3/5) = 5^(3 * 3/5) = 5^(9/5)
Step 3: Combine the Terms
Now, substituting these back into the expression gives:
(3^(-1/5) * 5^(-1/5)) * (3^(8/5) * 5^(8/5)) * (5^(-8/5)) / (5^(9/5))
Combine like bases:
- For base 3: 3^(-1/5 + 8/5) = 3^(7/5)
- For base 5: 5^(-1/5 + 8/5 - 8/5 - 9/5) = 5^(-10/5) = 5^(-2)
Final Result
Thus, the simplified expression is:
3^(7/5) / 5^(2).
This can be further expressed as 3^(7/5) * 5^(-2) or 3^(7/5) / 25.
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Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.?
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Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.?.
Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify 15 power minus 1 by 5 multiply 225 power 4 by 5 multiply 625 power minus 2 by 5 divided by 125 power 3 by 5.?.
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