Final answer:
To simplify the expression (27/125)^(-2/3) * (27/125)^(4/3), first combine the two terms by adding their exponents. Then simplify further using the property (a/b)^c = (a^c)/(b^c). Finally, apply the property (a^m)^n = a^(m * n) to obtain the simplified expression 27/125.
Step-by-step explanation:
To simplify the expression, we can combine the two terms by adding their exponents. Using the property (a^b)^c = a^(b * c), we can simplify (27/125)^(-2/3) * (27/125)^(4/3) as (27/125)^((-2/3) + (4/3)).
Using the property (a/b)^c = (a^c)/(b^c), we can further simplify the expression as (3^3/5^3)^(2/3).
Finally, using the property (a^m)^n = a^(m * n), we can simplify as 3^(3 * 2)/(5^(3 * 2)). This results in the simplified expression 27/125.
Learn more about Simplifying exponents