SIMPLIFYING MONOMIALS WITH EXPONENTS

To simplify monomials with exponents, we should be aware of the rules of exponents.

The Required Rules of Exponents are below.

Example 1 :

12x53x2

Solution :

12x53x2 aman = am-n= 4x5-2= 4x3

Example 2 :

-24cd3-6cd

Solution :

-24cd3-6cd aman = am-n= 4d3-1= 4d2

Example 3 :

36m64m2

Solution :

36m64m2= 9m6-2

Example 4 :

28m2n5-7m2n3

Solution :

28m2n5-7m2n3= -4n5-3= -4n2

Example 5 :

54a8-6a2

Solution :

= 54a8-6a2= -9a8-2= -9a6

Example 6 :

-32a3b6-4a3b2

Solution :

= -32a3b6-4a3b2= 8b6-2= 8b4

Example 7 :

3a4b26ab39a3b4

Solution :

3a4b26ab39a3b4Multiply the coefficients= 18a4b2ab39a3b4Combining like terms,18a4.ab2.b39a3b418a4b69a3b4= 2a4-3b6-4= 2ab2

Example 8 :

4m4n26m2n4-3m6n6

Solution :

4m4n26m2n4-3m6n6Multiply the coefficients= 24m4n2m2n4-3m6n6Combining like terms,24m4.m2n2.n4-3m6n624m8n8-3m6n6= -8m8-6n8-6= -8m2n2

Example 9 :

-9x3y68x7y42x2y3-6x3y

Solution :

-9x3y68x7y42x2y3-6x3yMultiply the coefficients, -72x3y6x7y4 -12x2y3x3yCombining like terms, -72x3.x7y6.y4 -12x2.x3y3.y 6x21y24 x6y3 6x21-6y24-3 6x15y21

Example 10 :

-7a2b44a3b5-2ab23

Solution :

-7a2b44a3b5-2ab23 -28a2.a3b4.b5-2a3b6 -28a6b20-2a3b6= 14a6-3b20-6= 14a3b14

Example 11 :

2xy233x5y44x2y5

Solution :

= 2xy233x5y44x2y5= 2x3y63x5y44x2y5= 6x3y6x5y44x2y5= 6x3.x5y6.y44x2y5= 6x15y244x2y5= 32 x15-2y24-5= 32 x13y19

Example 12 :

-3p2q5-4pq328p4q4

Solution :

= -3p2q5-4pq328p4q4= -3p2q5-4p2q68p4q4= 12p2q5p2q68p4q4= 12p2.p2q5.q68p4q4= 12p4q308p4q4= 128p4-4q30-4= 32p0q26= 32q26

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