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By what number should (⁻⁴/₅)⁻³ be divided to get the quotient as (¹⁶/₂₅)⁻²

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Final answer:

The number by which (⁻⁴/₅)⁻³ should be divided to get the quotient (¹⁶/₂₅)⁻² is -2/5.

Step-by-step explanation:

The given expression is (⁻⁴/₅)⁻³ and we need to find a number which when divided yields the quotient (¹⁶/₂₅)⁻². First, simplify these expressions: (⁻⁴/₅)⁻³ is equivalent to -(5/4)³ = -125/64 and (¹⁶/₂₅)⁻² is equivalent to (25/16)² = 625/256. Next, we can set up the equation -125/64 divided by our unknown number, let's call it x, equal to 625/256. Solving for x, we find that x equals -2/5.

Therefore, the number by which (⁻⁴/₅)⁻³ should be divided to get the quotient (¹⁶/₂₅)⁻² is -2/5.

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