Can you explain how to solve this equation? sqrt3((8/27)^-2)

First way:  work from the inside out:

A negative exponent means to flip the fraction:

( (8/27)^-2 )^1/3  =  ( (27/8)² )^1/3  =  ( 729/64 )^1/3  

Now find the cube root of both the numerator and the denominator:  9/4

Another way:  simplify the exponents first:

( (8/27)^-2 )^1/3  =   (8/27)^-2/3  =  (27/8)^2/3  

Find the cube root first:  (3/2)²  =  9/4

Thank you!