If you think back to your elementary school arithmetic class you will remember dividing 8 ÷ 2= 4. To prove that your answer was correct you would multiply 2 x 4 and if the answer to this multiplication problem equal 8 then you had done the division correctly.
With algebra you can follow the same procedure but we frequently deal with negative numbers and symbols. -10 ÷ 2 = -5 The easiest way to prove that the answer is correct and has the correct sign is to multiple the divisor 2 by the answer -5 the results will be -10. Hence you divided correctly.
If we divide a5 ÷ a2 = a5-2 which = a3 To prove our work we multiply a3 by a2 which = a3+2 = a5(remember in multiplication we add exponents and in division we subtract exponents.)
If we have numerical coefficients then we divide the numbers arithmetically.
If we divide -28a5 ÷ -4a2 = 7a5-2 which = 7a3 To prove our work we multiply 7a3 by -4a2 which = -28a3+2 = -28a5