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Monica [59]
3 years ago
15

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

Mathematics
1 answer:
vovikov84 [41]3 years ago
5 0

<u>Given</u><u> info</u><u>:</u><u>-</u><u> </u>What number should [(-5/3)³]^-3 be multiply obtain (-3/5)⁴ ?

<u>Explanation</u><u>:</u><u>-</u>

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

<u>The required number for the given problem is (-5/3)</u><u>⁵</u><u>.</u>

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