Question

By what number should (-3/2)power(-3) be divided so that the quotient may be (-8/27)power(-2)????

Answer 1

(-3/2)^-3÷x=(-8/27)^-2
(-2/3)^3÷x=(-27/8)^2
(-8/27)÷x=729/64
-8/27*1/x=729/64
-8/27x=729/64
-8/x=729*27/64
-8/x=19683/64
x/-8=64/19683
x=-512/19683

Answer 2

Answer: $(-\frac{2}{3})^9$

Step-by-step explanation:

Let x bet the required number,

According to the question,

$\frac{(-3/2)^{-3}}{x} = (\frac{-8}{27})^{-2}$

$\implies (\frac{-3}{2})^{-3}=x\times (\frac{-8}{27})^{-2}$

$\implies \frac{(\frac{-3}{2})^{-3}}{(\frac{-8}{27})^{-2}}=x$

$\implies \frac{((\frac{-8}{27})^{2}}{(\frac{-3}{2})^3}=x$

$\implies \frac{64/729}{-27/8}=x$

$\implies -\frac{512}{19683}=x$

$\implies -\frac{2^9}{3^9}=x\implies x = (-\frac{2}{3})^9$

Which is the required answer.