Final answer:
To find the least common multiple (LCM) of the two expressions 6w⁷u⁸v² and 8u⁵v³, you need to factorize each expression into its prime factors and then find the highest power of each prime factor that appears in either expression. The LCM will be the product of all the prime factors with their highest power.
Step-by-step explanation:
To find the least common multiple (LCM) of the two expressions 6w⁷⁷u⁸v² and 8u⁵v³, we need to factorize each expression into its prime factors and then find the highest power of each prime factor that appears in either expression.
Factoring the first expression, we have 6w⁷⁷u⁸v² = 2 × 3 × w × w × w × w × w × w × u × u × u × u × u × u × u × v × v
Factoring the second expression, we have 8u⁵v³ = 2 × 2 × 2 × u × u × u × u × u × v × v × v
Now, we can see that the LCM will be the product of all the prime factors with their highest power: LCM = 2 × 2 × 2 × 3 × w × w × w × w × w × w × w × u × u × u × u × u × u × u × v × v × v × v × v × v
The simplified form of the LCM is 8w⁷⁷u⁸v³.