Question

by what number should (-3/2)^_3 be divided so that the qoutient may be (-8/27)^_2

Answer 1

Let's assume the number as x

According to Question,

(- 3 / 2)⁻³ ÷ x = (- 8 / 27)⁻²

⇒ (- 2 / 3)³ = (- 27) / 8)² × x

⇒ (- 2)³ / 3³ = (- 27)² / 8² × x

⇒ (- 8) / 27 = 729 / 64 × x

⇒ x = { (- 8) / 27 × 64 / 729 }

⇒ x = (- 512 / 19,683 )

Hence,

The required number is (- 512 / 19,683)

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