Question

Answer this please with full explanation and procedure

Answer 1

let the number be x
then,
-3/2^3×x=-8/27^2
=-27/8x=729/64
x=729/64×8/27
x = 27/8

Answer 2

Answer:

$\bigg(\dfrac{2}{-3}\bigg)^9$

Step-by-step explanation:

Relationship between the dividend, divisor and quotient:

a ÷ b = c

⇒ b = a ÷ b

Define x:

Let the number be x

The question:

$\bigg(\dfrac{-3}{2} \bigg)^{-3} \div x = \bigg(\dfrac{-8}{27} \bigg)^{-2}$

Make x the subject:

$x = \bigg(\dfrac{-3}{2} \bigg)^{-3} \div \bigg(\dfrac{-8}{27} \bigg)^{-2}$

Write divide fraction as multiplication fraction:

$x = \bigg(\dfrac{-3}{2} \bigg)^{-3} \times \bigg(\dfrac{27}{-8} \bigg)^{-2}$

Write in positive index:

$= \bigg(\dfrac{2}{-3} \bigg)^{3} \times \bigg(\dfrac{-8}{27} \bigg)^{2}$

Write in index form:

$= \bigg(\dfrac{2}{-3} \bigg)^{3} \times \bigg(\dfrac{(-2)^3}{(3)^3} \bigg)^{2}$

(a/b)ⁿ = aⁿ/bⁿ:

$=\dfrac{2^3}{(-3)^3}\times \dfrac{((-2)^3)^2}{((3)^3)^2}$

(aˣ)ⁿ = aˣⁿ:

$=\dfrac{2^3}{(-3)^3}\times \dfrac{(-2)^6}{(3)^6}$

Evaluate the negative signs:

$=\dfrac{2^3}{-(3)^3}\times \dfrac{(2)^6}{(3)^6}$

aⁿ x aˣ = aⁿ⁺ˣ:

$=\dfrac{2^{3+ 6}}{-(3)^{3 + 6}}$

$=\dfrac{2^{9}}{-(3)^{9}}$

aⁿ/bⁿ =  (a/b)ⁿ

$=\bigg(\dfrac{2}{-3}\bigg)^9$

$\text {Answer: }\bigg(\dfrac{2}{-3}\bigg)^9$