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Compare which of the two is greater (100...

Compare which of the two is greater `(100)^(1/100) and (101)^(1/101)`

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Compare which of the two is greater (100)^((10)/(10)) and (101)^((1)/(101))

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If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=(3pi)/2 , then the value of x^(100)+y^(100)+z^(100)-9/(x^(101)+y^(101)+z^(101))