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Question
Prove that:
`((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
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Solution
We have to prove that `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
Let x = `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)`
`=(1-((0.1xx10)/(1xx10))^-1)/((3^-1/2^(3xx(-1)))(3^3/2^3)+((-1)^-1/3^-1))`
`=(1-1/10^-1)/((3^-1/2^-3)(3^3/2^3)+((-1)/(1/3^1)))`
`=(1-1/(1/10))/((3^(-1+3)/2^(-3+3))+(-1xx3/1))`
`=(1-1xx10)/(3^2/2^0+(-3))`
`=(1-10)/(3^2/1-3)`
`=(-9)/(9-3)`
`=(-9)/6`
`=(-3)/2`
Hence, `((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2`
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