If 2160 = 2^a.3^b.5^c, find a, b and c. Hence, calculate the value of 3^a × 2^-b × 5^-c.
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Question

If 2160 = 2^a.3^b.5^c, find a, b and c. Hence, calculate the value of 3^a × 2^-b × 5^-c.

KnowledgeBoat · Accepted Answer

Factorizing 2160, we get : ⇒ 2160 = 2⁴ × 3³ × 5¹ ⇒ 2^a.3^b.5^c = 2⁴ × 3³ × 5¹ ⇒ a = 4, b = 3 and c = 1. Substituting values of a, b and c in 3^a × 2^-b × 5^-c, we get : Hence, a = 4, b = 3 and c = 1 and 3^a × 2^-b × 5^-c = .

Mathematics

If 2160 = 2^a.3^b.5^c, find a, b and c. Hence, calculate the value of 3^a × 2^-b × 5^-c.

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