Final answer:
To evaluate 2⁻⁴/4⁰, simplify the numerator and denominator separately. The fraction 2⁻⁴ becomes 1/16, and the fraction 4⁰ becomes 1. Therefore, the expression simplifies to 1/16 divided by 1, which is 1/16. The fraction (27)⁻²/³ simplifies to 1/9.
Step-by-step explanation:
To evaluate the expression 2-4/40, we need to simplify both the numerator and the denominator first.
Starting with the numerator, 2-4, we know that a negative exponent indicates division. So, 2-4 is equal to 1/24. Evaluating 24, we get 16. Therefore, 2-4 is equal to 1/16.
Next, the denominator is 40, which is equal to 1.
So, the expression 2-4/40 simplifies to 1/16 divided by 1, which is just 1/16.
Therefore, the answer is 1/16.
For the second expression (27)-2/3, we can rewrite it as (33)-2/3. When we raise a power to another power, we multiply the exponents. So, (33)-2/3 is equal to 3(3 * -2/3) = 3-2.
Since a negative exponent indicates division, 3-2 is equal to 1/32 = 1/9.
Therefore, the answer is 1/9.