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Answer :
The correct expressions equivalent to the product of 10x9 and (60x–6)−1 are 10x9/(60x–6) and 10x9*(60x–6)−1.
The question asks which expressions are equal to the product of 10x9 and (60x–6)−1. To understand which expressions are equivalent, it's crucial to recall how negative exponents and division operations work in algebra.
Negative exponents denote a division, therefore, an expression like a−n is equivalent to 1/an. Thus, (60x–6)−1 is the same as 1/(60x–6). Multiplying this by 10x9 gives us 10x9/(60x–6).
Comparing the given options:
10x9/(60x–6) is correct since it represents the division as described.
10x9*(60x–6) shows direct multiplication without consideration of the negative exponent, therefore incorrect.
10x9*(60x–6)−1 is another way to write the original expression, making it correct.
10x9/(60x–6)−1 is incorrect because it suggests subtracting 1 after the division, which alters the meaning.
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