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प्रश्न
Simplify the following:
`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`
उत्तर
`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`
= `(3^3/7^3)^(2/3) ÷ (1)/(((5^4)/(2^4 xx 3^4))^(1/4)) xx (2^3 xx 67)/root(3)(3^3)`
= `(3^3/7^3)^(2/3) ÷ (1)/(((5^4)/(2^4 xx 3^4))^(1/4)) xx (2^3 xx 67)/(3^3)^(1/3)`
= `(3^(3xx2/3)/(7^(3xx2/3))) ÷ (1)/((5^(4xx1/4)/(2^(4xx1/4) xx 3^4xx1/4))) xx (2^3 xx 67)/(3^(3xx1/3)` .....(Using (am)n = amn)
= `(3^2/7^2) ÷ (1)/((5^1/(2^1 xx 3^1))) xx (2^3 xx 67)/(3^1)`
= `(3^2/7^2) ÷ ((2^1 xx 3^1)/5^1) xx ((2^3 xx 67)/(3^1))` ......(Using am x an = am+n and am ÷ an = am-n)
= `(3^2/7^2) ÷ (5^1/(2^1 xx 3^1)) xx ((2^3 xx 67)/(3^1))`
= `3^(2-1-1) xx 2^(3-1) xx 5^1 xx 7^2 xx 67`
= 30 x 22 x 51 x 72 x 67
= 1 x 4 x 5 x 49 x 67 ......(Using a0 = 1)
= 65660.
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