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Question
Find the value [4–1 + 3–1 + 6–2]–1 = ______.
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Solution
Find the value [4–1 + 3–1 + 6–2]–1 = `underlinebb(18/11)`.
Explanation:
Using law of exponents,
`a^-m = 1/a^m` ...[∵ a is non-zero integer]
∴ `[4^-1 + 3^-1 + 6^-2]^-1 = (1/4 + 1/3 + 1/36)^-1`
= `((9 + 12 + 1)/36)^-1` ...[∵ LCM of 4, 3 and 36 = 36]
= `(22/36)^-1`
= `36/22`
= `18/11`
Hence, [4–1 + 3–1 + 6–2]–1 = `18/11`
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