Question

Write \[\left( \frac{1}{9} \right)^{- 1/2} \times (64 )^{- 1/3}\] as a rational number.

Answer 1

We have to find the value of . `(1/9) ^((-1)/2) xx (64) ^((-1)/3`So,

`(1/9) ^((-1)/2) xx (64) ^((-1)/3` = `(1/9) ^((-1)/2) xx (64) ^((-1)/3`,

`= (1/3) ^((-1)/2) xx (4^3) ^((-1)/3) `

`= (1/3^(2 xx (-1)/2)) xx (4^(3 xx (-1)/3))`

`= (1/3^(2 xx (-1)/2)) xx (4^(3 xx (-1)/3))` 

`(1/9) ^((-1)/2) xx (64) ^((-1)/3 ) = 1/3^(-1) xx 4^(-1) `

                           `=1/(1/3) xx 1/4`

                           `= 1xx 3/1 xx 1/4`

                            `= 3/4`

Hence the value of the value of `(1/9)^(-1/2) xx (64)^(-1/3)` is `3/4`.