Respuesta :
The products of the given monomials are
i. 90a⁵b⁵c⁹
ii. x⁴y⁴
iii. 50x¹¹y³z
iv. 80b⁴c⁴
v. 30m⁵n⁷
Product of monomials
From the question, we are to determine the products of each of the three monomials
i. 9ab²c⁵, 2a³b²c² and 5abc²
9ab²c⁵ × 2a³b²c² × 5abc²
= 9 × 2 × 5 × a × a³ × a × b² × b² × b × c⁵ × c² × c²
= 90 × a⁵ × b⁵ × c⁹
= 90a⁵b⁵c⁹
ii. xy², x²y and xy
xy² × x²y × xy
= x × x² × x × y² × y × y
= x⁴ × y⁴
= x⁴y⁴
iii. 5x⁵, y²x⁵ and 10xyz
5x⁵ × y²x⁵ × 10xyz
= 5 × 10 × x⁵ × x⁵ × x × y² × y × z
= 50 × x¹¹ × y³ × z
= 50x¹¹y³z
iv. (-4b²c), (-2bc) and 10c²b
(-4b²c) × (-2bc) × 10c²b
= -4b²c × -2bc × 10c²b
= -4 × b² × c × -2 × b × c × 10 × c² × b
= -4 × -2 × 10 × b² × b × b × c × c × c²
= 80 × b⁴ × c⁴
= 80b⁴c⁴
v. Multiply (-5m²n²) by (-6m³n⁵)
(-5m²n²) × (-6m³n⁵)
= -5m²n² × -6m³n⁵
= -5 × m² × n² × -6 × m³ × n⁵
= -5 × -6 × m² × m³ × n² × n⁵
= 30 × m⁵ × n⁷
= 30m⁵n⁷
Hence, the products of the given monomials are
i. 90a⁵b⁵c⁹
ii. x⁴y⁴
iii. 50x¹¹y³z
iv. 80b⁴c⁴
v. 30m⁵n⁷
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