Question

What number should {(-5/3)^3}^-3 be Multiply to obtain (-3/5)^4.​

Answer 1

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.