Final Answer:
The value of a + b in the expression in the form axᵇ is 11.
Step-by-step explanation:
To represent the given product in the form axᵇ, we have: (2^3) * (5^4) * (7^1) = 2^3 * 5^4 * 7^1 = 8 * 625 * 7 = 3500. Therefore, a = 3500, and to express this in the form axᵇ, we factorize 3500. It breaks down to 2^2 * 5^3 * 7^2. Hence, a = 2^2 * 5^3 * 7^2 = 4 * 125 * 49 = 24500. From this representation, we derive that a = 24500, and in the form axᵇ, a = 24500, and b = 0. Therefore, the sum of a + b = 24500 + 0 = 24500.
In the given expression, breaking down the product into its prime factors, we find that it equals 2^3 * 5^4 * 7^1. After simplifying these exponents, we get 8 * 625 * 7, which equals 3500.
To express this in the form axᵇ, we further factorize 3500 into its prime factors, resulting in 2^2 * 5^3 * 7^2, where a = 24500 and b = 0. As per the form axᵇ, the value of a is 24500, and since b equals 0, the sum a + b = 24500 + 0 = 24500.