Final answer:
To evaluate the expression ((1)/(729))⁽⁻⁴ˣ⁻²⁾, simplify the base and the exponent. The simplified expression is 1/6561, not equal to 2187⁽²ˣ⁻⁷⁾.
Step-by-step explanation:
To evaluate the given expression, ((1)/(729))⁽⁻⁴ˣ⁻²⁾, we need to simplify both the base and the exponent. Firstly, let's simplify the base: (1)/(729) is equal to 1/3³. Now, let's simplify the exponent: (-4) x (-2) is equal to 8. So, the expression becomes (1/3³)⁸.
Using the property of exponents, we can rewrite (1/3³)⁸ as 1⁸ divided by (3³)⁸. Since any number raised to the power of 8 is equal to itself, 1⁸ is equal to 1. Next, (3³)⁸ is equal to 3⁸, which is equal to 6561.
Therefore, the simplified expression is 1/6561. So, the given expression ((1)/(729))⁽⁻⁴ˣ⁻²⁾ is equal to 1/6561. This means that it is not equal to 2187⁽²ˣ⁻⁷⁾.