Why do you subtract exponents when dividing powers with the same base?

Because the factors in the numerator cancel with the factors in the denominator. Consider this example:

All of the 6's in the denominator canceled with the 6's in the numerator, and only 3 6's "survived". The opposite can also happen, if there are more terms in the denominator:

So, everything is coherent

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5