Problem A: (7x^2-x-2)-(-6x^3+3)
You can consider the subtraction similiar to a -1(-6x^3+3). The 1 is implied. So to distribute that negative, we multiply this out.
-6x^3+3 becomes 6x^3 - 3
Our problem is now: 7x^2-x-2 + 6x^3 - 3
Now we add together like items. Let's rearrange for our sanity.
+ 6x^3 + 7x^2 - x - 2 - 3
Simplify: 6x^3 + 7x^2 - x - 5
Unfortionately, outside of factoring or something along those lines, that's as simple as we can get it. So the answer is A.
Problem B: f^2*f^4
Math rules tell us when we multiply the same bases with exponents, we add the exponents together. But the base doesn't change.
4+2 = 6. So: f^6 (D)
That's the easy answer: Math rules say so.
To expand on that specific rule, consider x^2 * x^3. What at the root are these saying? Multiply 2 copies of X, and then multiply 3 copies of x.
We can rewrite this same equation as x*x * x*x*x.
Remember that since all of these are multiplication, there is no order of operations that needs to be followed.
If we were simplifying that version of the equation, we would write x ^ 5.
