DIVISION

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 = a^5-2 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 = 7a^5-2 which = 7a³ To prove our work we multiply  7a³ by -4a² which = -28a³⁺² = -28a⁵

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