Question

Please tennetiraj86 please answer this I will Mark you brainlist​

Answer 1

Explanation:

Given :-

The number [(-5/3)³]^-3

To find :-

Find the number should [(-5/3)³]^-3 be multiply obtain (-3/5)⁴ ?

Solution :-

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

Answer:-

The required number for the given problem is (-5/3)⁵

Check :-

The number = (-5/3)⁵

According to the given problem

=> (-5/3)⁵× [(-5/3)³]^-3

=> (-5/3)⁵×(-5/3)^-9

Since (a^m)^n = a^mn

=> (-5/3)^(5+(-9))

Since a^m × a^n = a^(m+n)

=> (-5/3)^-4

=> (-3/5)⁴

Since a^-n = 1/a^n

Verified the given relations in the given problem

Used formulae:-

• (a^m)^n = a^mn

• a^-n = 1/a^n

• a^m / a^n = a^(m-n)

• a^m × a^n = a^(m+n)