Operations in algebra (Multiplication and Division)

Multiplication and division in algebra rests on exponents and ordinary division. The ordinary division is applied to coefficients and the exponents are applied to symbolic constants and variables. Exponents are result of successive multiplication. Some rules of exponents that are useful in multiplication and division of algebra are:

1. a^maⁿ = a^m+n
2. a^m/aⁿ = a^m−n
3. 1/a^m = a^−m

Here the first rule is useful in multiplication and the second rule is useful in division. One more important point is to be noted here. The law of multiplication for exponents is applied on similar symbolic constants and variables. Similar is the case for division. All the symbolic constants and variables are grouped and the law of exponents are applied. Then the different symbolic constants are multiplied or divided as the case may be.

Procedure for division and multiplication in algebra

1. Group the symbolic constants and variables.
2. Perform the division or multiplication on coefficients.
3. Apply the rule of exponents for similar symbolic constants and variables.
4. Solve.

Example 1:
Multiply 2a²b³ and 5a³b²
2a²b³×5a³b²
= 2×5a²a³b³b²
= 2×5a⁽²⁺³⁾b⁽³⁺²⁾
= 10a⁵b⁵

Divide 2a²b³ by 5a³b²
2a²b³/(5a³b²)
= (2/5)a²b³×a⁻³b⁻²
= (2/5)a²a⁻³b³b⁻²
= (2/5)a⁽²⁻³⁾b⁽³⁻²⁾
= (.4)a⁻¹b¹