answer this quick please
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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.
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