Final answer:
To evaluate the expression, we need to simplify each fraction with a negative exponent. 1/3-³ becomes 1/27, 1/2-³ becomes 1/8, and 1/4-³ becomes 1/64. We can then combine the fractions and calculate the result, which is -26/27.
Step-by-step explanation:
To evaluate the expression, we need to simplify each fraction with a negative exponent. Let's start with 1/3-3.
Recall that a negative exponent is equivalent to putting the item in the denominator. So, 1/3-3 = (3/1)³. Now, we can simplify this as (1/3)³ = (13)/(3³) = 1/27.
Next, let's simplify 1/2-³ Similarly, we write it as (2/1)³ = (1/2)³ = (13)/(2³) = 1/8.
Now, let's simplify 1/4-³. Again, we rewrite it as (4/1)³ = (1/4)³ = (13)/(4³) = 1/64.
Finally, we can evaluate the expression: 1/27 - 1/8 ÷ 1/64 = (1/27) - (1/8) × (64/1). Simplifying further, we get (1/27) - (1/8) × (8/1) = 1/27 - 1 = -26/27.