Final answer:
To evaluate (243/32) to the power of -0.4, recognize that 243 = 3^5 and 32 = 2^5, then apply the laws of indices to simplify to 3^-2/2^-2, which further simplifies to 4/9.
Step-by-step explanation:
To evaluate (243/32) to the power of -0.4 using the laws of indices, we first need to recognize that both 243 and 32 can be written as powers of 3.
Specifically, 243 is 35 and 32 is 25.
Applying the law of indices to rewrite the expression as a single power of 3, we have (35/25)-0.4.
Using the law that (a/b)n = an/bn, we can rewrite the expression as 35*-0.4/25*-0.4 which simplifies to 3-2/2-2.
Since a negative exponent means that the base needs to be in the denominator, we invert both fractions to get 22/32, or 4/9.
Therefore, the original expression evaluates to 4/9.