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Note: `(sqrt(3))^5 xx 9^2` `= 3^a xx 3sqrt(3) => (31^(1∕2)^5 xx (3^2)^2` `= 3^a xx 3^1 xx 3^(1/2)` `:. 3^(5∕2) xx 3^4` `= 3^a xx 3^1 xx 3^(1∕2) or 3^(5/2 + 4)` `= 3^((a + 1 + 1/2))` `or 3^(13∕2)` `= 3^(a + 3/2). So, a + 3/2` `= 13/2 or a = (13/2 - 3/2)` `= 5 `

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Note: Given Exp.` = (1/(1 + x^n/x^m) + 1 + x^m/x^n)` `= (x^m)/((x^m + x^n)) + (x^n)/((x^m + x^n))` `= ((x^m + x^n)/(x^m + x^n))` `= 1`

Note: `sqrt(x^(-1 y) . sqrt(y^(-1) z . sqrt(z^(-1) x` `= sqrt(x/y) . sqrt(z/y) . sqrt(x/z)` `= sqrt(y)/sqrt(x) xx sqrt(z)/sqrt(y) xx sqrt(x)/sqrt(z)` `= 1`

Note: Given Exp. `= 1/(1 + x^b/x^a + x^c/x^a) + 1/(1 + x^a/x^b + x^c/x^b) + 1/(1 + x^b/x^c + x^a/x^c) `= (x^a/(x^a + x^b + x^c) + x^b/(x^b + x^a + x^c) + x^c/x^c + x^b + x^a)` `= ((x^a + x^b + x^c)/(x^a + x^b + x^c)) = 1`

Note: Given Exp.` x = x^(b - c)(b + c - a) .x^(c - a)(c + a - b) .x^(a - b)(a + b - c)` `= x^((b^2 - c^2) + (c^2 - a^2) + (a^2 - b^2)) . x^(-a (b - c) - b (c - a) - c(a - b))` `= x^0 .x^0 = 1.

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Note: `= x^(b - c)(b + c - a) .x^(c - a)(c + a - b) . x^(a - b)(a + b - c)` `= x^((b^2 - c^2) + (c^2 - a^2) + (a^2 - b^2)) . x^(- a(b - c) - b(c - a) - c(a - b)` `= x^0 . x^0 = 1`