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

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Answer 1 · 2017-10-28T23:47:47

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

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.