Final answer:
To solve (w⁸-w⁶)/(w⁶-w⁵) with w = 40, first factor out common terms and simplify the expression. After substituting w = 40 into the simplified form, the calculation results in the final answer of 160, which is option b.
Step-by-step explanation:
To compute the value of (w⁸-w⁶)/(w⁶-w⁵) with w = 40, we should first simplify the expression by factoring out the common terms. Let's first factor w⁶ out of the numerator and w⁵ out of the denominator.
The expression becomes:
w⁶(w²-1)/w⁵(w-1)
Now, we can simplify it by cancelling out w⁵ from both the numerator and the denominator. This leaves us with:
w(w²-1)/(w-1)
Now, we substitute w = 40 and simplify the remaining expression:
(40)(40²-1)/(40-1)
This simplifies to:
(40)(1600-1)/39
And further to:
(40)(1599)/39
When we perform the calculations, we get:
1599×40/39
The final answer turns out to be 160, which corresponds to option b.