Question

By what number should (-3/2)^-3 be divided so that the quotient may be (4/27)^-2 ?​

Answer 1

Answer:

let the no. be x

(-3/2)^-3 ÷ x = (4/27)^-2

x = (4/27)^-2 × (-3/2)^-3

now we'll make the power positive

x = (27/4)^+2 × (4/-3)^+3

x = 729 / 16 × 16/-27

x = -27/2

Answer 2

Let the no be x

ATQ

${ \frac{ - 3}{2} }^{ - 3} \div x = { \frac{4}{27} }^{ - 2}$

Now by cross multiplication

$729 \times 27x = - 8 \times 16$

$19683x = - 128$

$x = \frac{ - 128}{19683}$

$x = \frac{ - 128}{ {27}^{3} }$

Therefore the answer is

$\frac{ - 128}{ {27}^{3} }$

Now lets verify it

(-3/2)^-3 ÷ -128/27³ = (4/27)^-2

(-2/3)^3 × -19683/128 = (27/4)^2

-8/27 × -19683/128 = 729/16

157464/3456 = 729/16

On simplyfying

729/16 = 729/16

Hence verified

Hope it is helpful

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