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Question
Prove that:
`(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3`
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Solution
We have to prove `(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3`
`(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=1^-2/4^-2-3xx2^(3xx2/3)xx4^0+3^(2xx-1/2)/2^(4xx-1/2)`
`=1/2^(2xx-2)-3xx2^2xx4^0+3^-1/2^-2`
`=1/2^-4-3xx2^2xx4^0+3^-1/2^-2`
`=1/(1/2^4)-3xx2^2xx4^0+(1/3)/(1/2^2)`
`=1xx2^4/1-3xx2^2xx1+1/3xx2^2/1`
`=16/1-12/1+4/3`
`=16/3`
Hence, `(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3`
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