Final answer:
To solve the expression, multiply the coefficients and add the exponents of like variables. The correct answer after combining them is 560u^4v^9, not the provided options. There was a correction made to the exponent of u.
Step-by-step explanation:
To calculate the expression 7v^3 * 10u^3 * v^3 * 8uv^3, you need to multiply the coefficients (numbers in front of the variables) and add the exponents of like variables together. Let's break it down:
- Multiply the coefficients: 7 * 10 * 8 = 560.
- Add the exponents of u: u^3 * u = u^(3+1) = u^4.
- Add the exponents of v: v^3 * v^3 * v^3 = v^(3+3+3) = v^9.
Now, combine the results to get the final answer:
560 * u^4 * v^9
However, we have made a mistake here because we have miscalculated the exponents of u; the correct exponents should be added as 3 (from u^3) + 1 (from u) to get u^4. Hence, the correct multiplication of the exponents of u gives us u^4. The final correct answer is Option A: 560u^4v^9.
Note: This solution contains a correction to the exponent of u, which should be u^4, not u^3 or u^6 as previously considered.