Вправи: 657

657. Спростіть вираз:

1) 45a3b • 5ab-1 = 45a3•5ab• b-1 = 225a4 = 15 • |a²| = 15a²;

2) 45a3b : 5ab-1 = 45a3b • b-15a = 45a3•b-1b•5a = 9a2b2 = 3|a||b| = 3ab;

3) 12x5y-2 : y63x-7 = 12x5y-2 • 3x-7y6 = 12x5• 3x-7y-2• y6 = 36x-2y4 = 36x2y4 = 6x•|y2| = 6xy2;

4) 12x5y-2 • y63x-7 = 12x5 •y6y-2• 3x-7 = 12x5• x73y-2• y-6 = 4x12y8 = 2|x⁶| • |y⁴| = 2x⁶y²;

5) 189•xyz-2 • xy-517z4 = 179•xyz-2 • xy-517z4 = 17xy• xy-59z-2•17z4 = x2y-49z2 = x29y4z2 = |x|3y2•|z| = |x|3y2|z|;

6) ab3cd-4 • c-3a-5 • d-4c-4a6 = ab3•c-3•d-4cd-4•a-5•c-4a6 = ab3•d4•a5c4c•c3•a6 = a6b3c4d4a6c4 = b3d4 = b2•b•d4 = |b|b • |d²| = bb • d².