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प्रश्न
Evaluate the following:
`(25/9)^(3/2) + (27/64)^(-1/3)`
मूल्यांकन
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उत्तर
Given: `(25/9)^(3/2) + (27/64)^(-1/3)`
Step-wise calculation:
1. Calculate `(25/9)^{3/2)`:
`(25/9)^(3/2) = ((25/9)^(1/2))^3`
`(25/9)^(3/2) = (sqrt(25)/sqrt(9))^3`
`(25/9)^(3/2) = (5/3)^3`
`(25/9)^(3/2) = 125/27`
2. Calculate`(27/64)^(-1/3)`:
`(27/64)^(-1/3) = (64/27)^(1/3)`
`(27/64)^(-1/3) = (root(3)(64))/(root(3)(27))`
`(27/64)^(-1/3) = 4/3`
3. Add the two results:
`125/27 + 4/3 = 125/27 + (4 xx 9)/(3 xx 9)`
`125/27 + 4/3 = 125/27 + 36/27`
`125/27 + 4/3 = (125 + 36)/27`
`125/27 + 4/3 = 161/27`
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