Given info:- What number should [(-5/3)³]^-3 be multiply obtain (-3/5)⁴ ?
Explanation:-
Given number = [(-5/3)³]^-3
Let the required number be X
On multiplying [(-5/3)³]^-3 with X
⇛ [(-5/3)³]^-3 × X
According to the given problem
The result = (-3/5)⁴
⇛ [(-5/3)³]^-3 × X = (-3/5)⁴
⇛ (-5/3)^(3×-3) × X = (-3/5)⁴
Since (a^m)^n = a^mn
⇛ (-5/3)^-9 ×X = (-3/5)⁴
⇛(-3/5)⁹ ×X = (-3/5)⁴
Since a^-n = 1/a^n
⇛X = (-3/5)⁴/(-3/5)⁹
⇛X = (-3/5)^(4-9)
Since a^m / a^n = a^(m-n)
⇛ X = (-3/5)^-5
⇛ X = (-5/3)⁵
Since a^-n = 1/a^n
Therefore, X = (-5/3)⁵
The required number for the given problem is (-5/3)⁵.
