Answer:
1st Tile = 144m²n³
2nd tile = [tex]72m^{4}n^{4}[/tex]
3rd tile = [tex]36m^{3}n[/tex]
4th tile = [tex]48m^{4}n^{4}[/tex]
Step-by-step explanation:
In this question we have to find out the least common multiple of the denominators and pair them with the rational expressions.
LCM of 9m²n and 16mn²
prime factors of 9m²n = 3×3×m×m×n
prime factors of 16mn³ = 2×2×2×2×m×n×n×n
So LCM of both = 2×2×2×2×3×3×m×m×n×n×n = 144 m²n³
LCM of [tex]8m^{4}n^{2}, 18m^{2}n^{4}[/tex]
prime factors of [tex]8m^{4}n^{2}[/tex] = 2×2×2×m×m×m×m×n×n
prime factors of [tex]18m^{2}n^{4}[/tex] = 2×3×3×m×m×n×n×n×n
LCM of both = 2×2×2×3×3×m×m×m×m×n×n×n×n = [tex]72m^{4}n^{4}[/tex]
Similarly LCM of [tex]12mn, 18m^{3}n[/tex] will be [tex]36m^{3}n[/tex]
LCM of [tex]24mn^{4}, 16m^{4}n[/tex] will be [tex]48m^{4}n^{4}[/tex]
