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प्रश्न
Evaluate:
`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`
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उत्तर
`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`
`=("a"^(2"n"+1)xx"a"^(4"n"^2-1))/("a"^(4"n"^2-"n")xx"a"^(4"n+6"`
`="a"^(4"n"+2"n")/("a"^(4"n"^2+3"n"+6)`
`="a"^(4"n"^2+2n-(4n^2+3n+6)`
`="a"^(4"n"^2+2n-4n^2-3n-6)`
`="a"^(-"n"-6)`
`="a"^-("n"+6)`
`=1/("a"^("n"+6)`
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`(27)^(2/3)÷(81/16)^(-1/4)`
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`[(64)^-2]^-3÷[{(-8)^2}^3]^2`
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`8^0+4^0+2^0`
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`(36"x"^2)^(1/2)`
Prove that:
`((x^a)/x^b)^(1/(ab))((x^b)/x^c)^(1/(bc))(x^c/x^a)^(1/(ca))=1`
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