Explain y u got the answer you very much.

ANS: power of a quotient property

(x/y)^n = x^n / y ^n   ( power of quotient )

x^m/x^n = x^(m-n) (Quotient of power) 

x^m x^n =  x^(m+n)   (Product of powers)   < Same base >

x^(m^n)   (Power of Power) 

In your case you have  (2/5)^3   -> 2/5 is called   a quotient ( fraction )  when you raise it to power  ( ^3) it's power of quotient

Power = multiple repetitions of multiplication 

(2/5)^3 = 2/5 multiplied by itself 3 times = 2/5 * 2/5 * 2/5 

 

in multiplication you simply multiply all terms in the denominator times each other and all terms in the nominator times each other


we know that repetitive multiplication = power , we have 3 terms in the denominator 2 2 2  

so = 2^3    ( 3 because it's repeated 3 times )

same for the denominator we get 5^3



2^3 = 2 x 2 x 2 = 8 

5^3 = 5 x 5 x 5  = 125

= 8/125

Proving such property in general requires the use of Proof by induction in which you have 3 basic steps < basic step (proof for 1 or 0) , assume true for n , proof for n + 1 or simple induction start from 0 repeat until you have a pattern and induce the general formula)

x/y * x/y  = x^2/y^2 = (x/y)^2

x/y * x/y * x/y = x^3/y^3 = (x/y)^3

......

x/y * x/y  * x/y * ...... n = (x/y)^n