Question

How do you simplify `(1/9)^(-3/2)`?

Answer 1

Using the formula `a ^ (-b) = (1 / a^b)`, and the formula `(a ^ m) ^ n = a ^ (mn)`, we obtain answer is 27.

Explanation:

We have, in our problem,

`(1/9) ^ (-3/2)` ( Expression 1 )

Rewrite the BASE `(1/9)` in our ( Expression 1 ), using the formula `a ^ (-b) = (1 / a^b)`, as

`(3 ^ (-2)) ^ (-3/2)` ( Expression 2 )

--------------- Observe that `3 ^ 2` is 9 and `3 ^(-2)` is `1/9` ----------------

Using the formula `(a ^ m) ^ n = a ^ (mn)`, we can rewrite our ( Expression 2 ) as

`3 ^ ((-2)*(-3/2))`

Simplify by multiplying (-2) by (-3/2) in the Exponent. We get, 3.

Hence, our ( Expression 2 ) can be written as

`3 ^ 3`

Which gives us 27.

Hence, ( Expression 1 ) when simplified yields 27.