SIMPLIFY RATIONAL EXPRESSIONS MONOMIALS

Simplify each expression.

Problem 1 :

21x218x

Solution:

= 21x218x=7×3×x×x2×3×3×x=7x6

Problem 2 :

24a40a2

Solution:

=24a40a2=2×2×2×3×a2×2×2×5×a×a=35a

Problem 3 :

32x38x4

Solution:

=32x38x4=2×2×2×2×2×x×x×x2×2×2×x×x×x×x=4x

Problem 4 :

16a512x9

Solution:

=16a512x9=2×2×2×2×a52×2×3×x9=4a53x9

Problem 5 :

15a3b225ab5

Solution:

=15a3b225ab5=3×5×a×a×a×b×b5×5×a×b×b×b×b×b=3a25b3

Problem 6 :

2x24x3

Solution:

=2x24x3=2×x×x2×2×x×x×x=12x

Problem 7 :

15x4y225x2y6

Solution:

=15x4y225x2y6=3×5×x×x×x×x×y×y5×5×x×x×y×y×y×y×y×y=3x25y4

Problem 8 :

6x2y55x310x43x2y7

Solution:

=6x2y55x3×10x43x2y7=2×3×x×x×y×y×y×y×y5×x×x×x×10×x×x×x×x3×x×x×y×y×y×y×y×y×y=4xy2

Problem 9 :

4a5b9a4÷6ab412b2

Solution:

=4a5b9a4÷6ab412b2=4a5b9a4×12b26ab4=2×2×a×a×a×a×a×b3×3×a×a×a×a×2×2×3×b×b2×3×a×b×b×b×b=89b

Problem 10 :

Multiply:

25x28y8 24y455x7

Solution:

=25x28y8 24y455x7=5×5×x×x2×2×2×y×y×y×y×y×y×y×y 2×2×2×3×y×y×y×y11×5×x×x×x×x×x×x×x=1511x5y4

Problem 11 :

Divide:

a4b2a÷b44

Solution:

=a4b2a÷b44=a4b2a×4b4=a×a×a×a×b×ba×4b×b×b×b=4a3b2

Problem 12 :

8x29 92

Solution:

=8x29 92=4x2

Problem 13 :

9n2n 75n

Solution:

=9n2n 75n=6310n

Problem 14 :

5x24 65

Solution:

=5x24 65=3x22

Problem 15 :

10p5÷810

Solution:

=10p5÷810=10p5×108=5p2

Problem 16 :

Add 7a3a2b+4b6ab4

Solution:

=7a3a2b+4b6ab4=7×a3×a×a×b+2×2×b2×3×a×b×b×b×b=73ab+23ab3=7b2+23ab3

Problem 17 :

Subtract 45a-7b4a2

Solution:

=45a-7b4a2Take LCM,=16a20a2-35b20a2=16a-35b20a2

Problem 18 :

Add 68a+4+3a8

Solution:

=68a+4+3a8By cross multiplication,=6×88(8a+4)+3a(8a+4)8(8a+4)=488(8a+4)+24a2+12a8(8a+4)=48+24a2+12a8(8a+4)=12+6a2+3a2(8a+4)=6a2+3a+1216a+8

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