Respuesta :
Respuesta:
Okay, let's start by substituting the given values of x and y into the expression 2/3x³ - 5/4y³ - 2.
First, substitute x = -1/2 and y = 1/3 into the expression:
2/3(-1/2)³ - 5/4(1/3)³ - 2
Now, let's simplify each part step by step:
First, calculate (-1/2)³:
(-1/2)³ = (-1)^3 / (2)^3
= -1 / 8
Now, substitute this value back into the expression:
2/3 * (-1/8) - 5/4 * (1/27) - 2
Next, simplify (-1/8) and (1/27):
2 * (-1/24) - 5/4 * (1/27) - 2
= -2/24 - 5/108 - 2
Now, simplify the fractions:
-1/12 - 5/108 - 2
To combine the fractions, we need to find a common denominator. The common denominator for 12 and 108 is 108.
Rewrite -1/12 as an equivalent fraction with a denominator of 108:
-9/108 - 5/108 - 2
Combine the fractions:
-9/108 - 5/108 - 216/108
= (-9 - 5 -216)/108
= -230 /108
Finally, simplify the fraction:
-230 /108 = -115 /54
So, when x = -1/2 and y = 1/3, the value of the expression 2/3x³ - 5/4y³ - 2 is equal to -115 /54.