By what number should (-2/3)^-3 be divided so that the quotient may be (4/27)^-2?
Please give the full working solution.
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Answer: -27/2
Let the required number be x.
Then,
A/q
(-2/3)^-3 / x = (4/27)^-2
=> 1/x = (4/27)^-2 / (-2/3)^-3
=> x = (-2/3)^-3 / (4/27)^-2
=> x = (-3/2)^3 / (27/4)^2
=> x = (-3/2)^3 / (3)^2* (9/4)^2
=> x = (-3/2)^3 / (3)^2* (-3/2)^2
=> x = (-3/2)^3-2 / (3)^2
=> x = (-3/2) / 9
=> x = -27/2
Step-by-step explanation:
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