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प्रश्न
Evaluate:
`(3^4 xx 12^3 xx 36)/(2^5 xx 6^3)`
उत्तर
We have, `(3^4 xx 12^3 xx 36)/(2^5 xx 6^3) = (3^4 xx (2^2 xx 3)^3 xx (2^2 xx 3^2))/(2^5 xx (2 xx 3)^3` ......[∵ 12 = 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3]
= `(3^4 xx 2^6 xx 3^3 xx 2^2 xx 3^2)/(2^5 xx 2^3 xx 3^3)` ......[∵ (a × b)m = am × bm]
= `((3^4 xx 3^2 xx 3^3) xx (2^6 xx 2^2))/((2^5 xx 2^3) xx 3^3)`
= `(3^(4+2+3) xx 2^(6+2))/(2^(5+3) xx 3^3)` ......[∵ am × an = am+n]
= `(3^9 xx 2^8)/(3^3 xx 2^8)` = 39–3 × 28–8 ......`[∵ a^m/a^n = a^(m-n)]`
= 36 × 20 = 36 × 1 ......[∵ a0 = 1]
= 729
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