Final answer:
Among the given options, only the first expression, 10x9/(60x−6), correctly represents the product of 10x9 and (60x−6)−1. It correctly places the term with the negative exponent in the denominator, following the rules for negative exponents.
Step-by-step explanation:
The student's question asks for all expressions equivalent to the product of 10x9 and (60x−6)−1. From the options provided, the correct expressions must take into account the rules of exponents and negative exponents. The expression (60x−6)−1 indicates that this term should be in the denominator based on the properties of negative exponents.
Looking at each option:
10x9/(60x−6) is correct because it places (60x−6)−1 in the denominator as indicated by the negative exponent.
10x9*(60x−6) multiplies the two terms, which is not what is asked.
10x9*(60x−6)−1 correctly denotes (60x−6)−1 as a factor with a negative exponent, but we should avoid multiplying these terms directly to adhere to the original expression.
10x9/(60x−6)−1 raises ambiguity with the placement of the negative exponent and would be mathematically incorrect as it suggests subtraction after division.
To summarize, the expression in scientific notation connects with rules governing negative exponents and exponents subtraction when diving quantities with exponents. Thus, only the expression in option 1 is correct as it exactly fits the requirement that the term with a negative exponent is in the denominator.