किंमत काढा 8⁵/³ - 4⁻⁵/² = ?
योग्य उत्तर पर्याय १ (A) (31(31) / (32)) आहे.
महत्त्वाचे मुद्दे (Key Points):
• पायरी १: 8⁵/³ चे रूप सोपे करणे:
• ८ = २^३, म्हणून (२^३)५/३ = २^५ = ३२.
• पायरी २: 4⁻⁵/² चे रूप सोपे करणे:
• ४ = २^२, म्हणून (२^२)⁻५/२ = २⁻५ = (१) / (२^५) = (१) / (३२).
• पायरी ३: वजाबाकी करणे:
• ३२ - (१) / (३२) = (१०२४ - १) / (३२) = (१०२३) / (३२) = ३१(३१) / (३२).
• महत्त्वाची टीप: ८^(५/३) = ३२, ४^(-५/२) = १/३२. ३२ - १/३२ = ३१ पूर्णांक ३१/३२.
The correct answer is Option A (31(31) / (32)).
Key Points:
• Step 1: Simplify 8⁵/³.
• Since 8 = 2³, we get (2³)⁵/³ = 2³ × (5/3) = 2⁵ = 32.
• Step 2: Simplify 4⁻⁵/².
• Since 4 = 2², we get (2²)⁻⁵/² = 2² × ^(-5/2) = 2⁻⁵ = (1/2⁵) = (1/32) .
• Step 3: Calculate difference.
• 8⁵/³ - 4⁻⁵/² = 32 - (1/32) = (1024 - 1/32) = (1023/32) = 31 (31/32) .
• Hence, Option 1 (31 (31/32) ) is the exact value.
• Key Takeaway: 8^(5/3) = 32, 4^(-5/2) = 1/32. 32 - 1/32 = 31 and 31/32.
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