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Question
`(16 xx 10^2 xx 64)/(2^4 xx 4^2)`
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Solution
Using laws of exponents,
am ÷ an = (a)m – n and am × an = am + n ...[∵ a is non-zero integer]
∴ `(16 xx 10^2 xx 64)/(2^4 xx 4^2) = (4)^2 xx 10^2 xx 2^-4 xx (4)^3 xx 4^-2` ...`[(∵ 64 = 4 xx 4 xx 4),(and 16 = 4 xx 4)]`
= (4)3 × 102 × 2–4
= (22)3 × 102 × 2–4
= 26 × 102 × 2–4
= 22 × 102 ...[∵ 22 = 4]
= 4 × 100
= 400
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