Final answer:
The product of the given expression is 75a⁴b¹³, which follows from multiplying the coefficients and adding the exponents of the like variables. None of the provided answer choices match this result, which may indicate an error in the provided options or a misunderstanding of the original question.
Step-by-step explanation:
The question is asking what the product of the given expression is: ((3a²b⁷)(5²° 6°)). To solve this, we need to multiply the coefficients (numeric parts) and add the exponents of the like variables following the law of exponents. The law states that when multiplying exponential terms with the same base, you keep the base and add the exponents.
First, we multiply the coefficients: 3 * 5² = 3 * 25 = 75.
Next, we add the exponents of the variable 'a': 2 + 2 = 4, so a to the power of 4 is a⁴.
Lastly, we add the exponents of the variable 'b': 7 + 6 = 13, so b to the power of 13 is b¹³.
Combining these, we get the final product: 75a⁴b¹³.
However, none of the answer options provided match this result. It seems there may have been an error in the options given or a misunderstanding of the question as written. If the question meant to ask for the product of (3a²b⁷) * (5² * 6), the answer would be 75a⁴b¹³, but this is not one of the provided options A) (8a⁵⁰₁₅) B) (8a⁶⁵₆) C) (15a⁵⁰₁₅) D) (15a⁵⁶₅₆).