Final answer:
To simplify 6v⁸*2y*2y³*v, multiply the coefficients for 24, add the exponents of like bases to get v⁹ and y⁴, and combine them to yield the simplified form 24v⁹y⁴.
Step-by-step explanation:
To multiply 6v⁸*2y*2y³*v, first, multiply the coefficients (numbers) and then the variables with the same base separately. The coefficients are 6, 2, and 2. Multiplying these together gives 6*2*2 = 24.
Next, look at the variables. v⁸ and v have the same base, so you add the exponents: 8 + 1 = 9. Thus, v⁸ * v is v¹.
The variable y also has an exponent, so multiply y*y³ by adding the exponents as well: 1 + 3 = 4, so y*y³ becomes y⁴.
Combine these results to get the final answer: 24v⁹y⁴.