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Question
Which one of the following is not equal to \[\left( \frac{100}{9} \right)^{- 3/2}\]?
Options
\[\left( \frac{9}{100} \right)^{3/2}\]
\[\left( \frac{1}{\frac{100}{9}} \right)^{3/2}\]
\[\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}\]
\[\sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}}\]
Solution
We have to find the value of `((100)/9)^(3/2)`
So,
`((100)/9)^(-3/2) = ((10^2)/3^2)^(-3/2`
`=(10^(2xx 3/2))/(3^(2xx 3/2))`
`= (10^(2xx 3/2))/(3^(2xx 3/2))`
`= 10^-3/3^-3`
`((100)/9)^(3/2) = (1/10^3)/(1/3^3)`
`=1/(10 xx 10 xx 10) xx (3xx3xx3)/1`
`= (3xx3xx3)/(10xx10xx10)`
Since, `(100/9)^(3/2)` is equal to `(9/100)^(3/2)`,, `1/((100/9)^(3/2))` `(3xx3xx3)/(10xx 10xx10)`.
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