Final answer:
Choice A is equivalent to \(\dfrac{1}{-7}\cdot\dfrac{-6}{5}\) because the negative sign's position does not affect the product's value. Choice B is not equivalent because the numbers in the product were changed incorrectly. Therefore, the correct answer is Choice A.
Step-by-step explanation:
The expressions equivalent to \(\dfrac{1}{-7}\cdot\dfrac{-6}{5}\) involve the multiplication of fractions and the rules concerning the signs of products. When multiplying two fractions, you multiply their numerators (top numbers) together and their denominators (bottom numbers) together. Additionally, the rules for multiplication of signs apply: a negative times a negative equals a positive, and a positive times a negative equals a negative.
Looking at Choice A \(-\dfrac{1}{7}\cdot\dfrac{6}{5}\), we observe that the only difference from the original expression is the position of the negative sign, which doesn't affect the value. Therefore, Choice A is equivalent to the original expression.
Choice B \(-6\cdot-\dfrac{7}{5}\) changes the numbers being multiplied; however, the overall product, when simplified, should reflect the multiplication of -1 by the original expression, resulting in an equivalent expression but with a positive sign. The actual computation of Choice B is not equivalent to the original expression, therefore Choice B is not equivalent.
Choice C None of the above is incorrect since we have already identified that Choice A is equivalent to the original expression.