Question

How do I simplify `(t^3)(t^(n-3))`?

Answer 1

`(t^3)(t^(n-3)) = t^(3+(n-3)) = t^n`

with some restrictions...

Explanation:

With certain restrictions, `a^b*a^c = a^(b+c)`

If `t = 0` then we require `n-3 > 0`, that is `n > 3`, in order that `t^(n-3)` be defined.

If `t < 0` then both the left and right sides of the equation are only defined if `n in ZZ`, but perhaps the variable name `n` is supposed to imply that anyway.