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Note: `p = 3/4 = 0.6, q = 7/9 = 0.777, i.e.r = 0.714` Clearly, `0.6 <0.714 < 0.777 i.e p< r < q.

Note: `(6)^(10) xx (7)^(17) xx (55)^(27)` `= 2^(10) xx 3^(10) xx 7^(17) xx 5^(27) xx 11^(27)` :. The total number of prime factors `= (10 + 10 + 17 + 27 + 27) = 91`

Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11

Note: `(6 + 6 + 7) - (2 + 8 + 9) = 0,` So, 978626 is divisible by 11

Note: `(1/6)^(12) xx (8)^(25) xx (3/4)^(15)` `= 1/(2^(12) xx 3^(12)) xx (2^3)^(25) xx 3^(15)/(2^15 xx 2^15)` `= (2^75 xx 3^15)/(2^42 xx 3^12)` `= 2^33 xx 3^3` :. Total number of prime factors `= (33 + 3) = 36`

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Note: Let the given number be x. The when divided by 32. suppose gives the quotient k. Then, `x = 32 k + 29 = 8 xx (4 k + 3) + 5` Thus, when x is divided by 8. it gives `(4 k + 3)` as quotient and 5 as remainder.