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Simplify : (81/16)^(-3/4) xx [(25/9)^(-3...

Simplify : `(81/16)^(-3/4) xx [(25/9)^(-3/2) -: (5/2)^(-3)`

Text Solution

Verified by Experts

`((81)/(16))^(-(3)/(4)) xx [((25)/(9))^(-(3)/(2)) div ((5)/(2))^(-3)] = ((3^(4))/(2^(4)))^(-(3)/(4)) xx [((5^(2))/(3^(2)))^(-(3)/(2)) div ((5)/(2))^(-3)]`
`=[((3)/(2))^(4)]^(-(3)/(4)) xx [ {((5)/(2))^(2)}^(-(3)/(2)) div ((5)/(2))^(-3)] = ((3)/(2))^(4xx(-(3)/(4))) xx[((5^(2))/(3^(2)))^(-(3)/(2)) div((5)/(2))^(-3)]`
`=((3)/(2))^(-3)xx[((5)/(3))^(-3) div ((5)/(2))^(-3)] = ((2)/(3))^(3) xx [((3)/(5))^(3) div((2)/(5))^(-3)]`
`= (2^(3))/(3^(3)) xx [(3^(3))/(5^(3)) div(2^(3))/(5^(3))] = (2^(3))/(3^(3)) xx [(3^(3))/(5^(3)) xx(5^(3))/(2^(3))] = (2^(3))/(3^(3))xx(3^(3))/(2^(3)) = 1`
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prove that ((81)/(16))^(-(4)/(4))*{((25)/(9))^(-(3)/(2))-:((5)/(2))^(-3)}=1

prove that ((81)/(16))^(-(4)/(4))*{((25)/(9))^(-(3)/(2))+((5)/(2))^(-3)}=1