Question

Which one of the following is not equal to \[\left( \frac{100}{9} \right)^{- 3/2}\]?

Options

• \[\left( \frac{9}{100} \right)^{3/2}\]

• \[\left( \frac{1}{\frac{100}{9}} \right)^{3/2}\]

• \[\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}\]

• \[\sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}}\]

Answer 1

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)`.