Question

answer this quick please
​

Answer 1

Step-by-step explanation:

Given:-

(-3/2)^-4

To find:-

By what number should (-3/2)^-4 be divided to get (-2/3)^3 ?

Solution:-

Given number = (-3/2)^-4

Let the required number be X

On dividing (-3/2)^-4 by X then

=> (-3/2)^-4/X

The result = (-2/3)^3

=> (-3/2)^-4/X = (-2/3)^3

=> (-3/2)^-4= (-2/3)^3×X

=>(-2/3)^3×X = (-3/2)^-4

=>X = [(-3/2)^-4]/[(-2/3)^3]

=>X = [(-3/2)^-4]×[(-3/2)^3]

We know that

a^m × a^n = a^(m+n)

Where a = (-3/2) ,m = -4 and n= 3

=> X = (-3/2)^(-4+3)

=>X= (-3/2)^-1

We know that

a^-n = 1/a^n

=>X= 1/(-3/2)

=> X=-2/3

Therefore,X = -2/3

Answer:-

The required number for the given problem is -2/3

Check:-

[(-3/2)^-4]/[-2/3)

=> [(-3/2)^-4]× (-3/2)

=> (-3/2)^(-4+1)

=> (-3/2)^-3

=> (-2/3)^3

Verified the given relation.