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प्रश्न
Simplify:
`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`
उत्तर
`(3^5 xx 10^5 xx 25)/(5^7 xx 6^5)`
= `(3^5 xx (2 xx 5)^5 xx 5 xx 5)/(5^7 xx 2^5 xx 3^5)`
= `(3^5 xx 2^5 xx 5^5 xx 5^2)/(5^7 xx 2^5 xx 3^5)` ...[∵ (a × b)m = am × bm]
= `(3^5 xx 2^5 xx 5^(5 + 2))` ...[∵ am × an = am + n]
= `(3^5 xx 2^5 xx 5^7)/(5^7 xx 2^5 xx 3^5)`
= 35 - 5 × 25 - 5 × 57 - 7 ...[∵ am ÷ an = am - n]
= 30 × 20 × 50
= 1 × 1 × 1
= 1
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