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Question
`(125 xx x^-3)/(5^-3 xx 25 xx x^-6)`
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Solution
Using laws of exponents,
am + an = (a)n – m and `a^-m = 1/a^m` ...[∵ a is non-zero integer]
∴ `(125 xx x^-3)/(5^-3 xx 25 xx x^-6) = (5)^3 xx 5^3 xx 5^-2 xx x^-3 xx x^6` ....`[(∵ 125 = 5 xx 5 xx 5),("and" 25 = 5 xx 5)]`
= 54 × x3
= 5 × 5 × 5 × 5 × x3 ...[∵ am × an = am + n]
= 625 x3
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