Question

Find the value of (x/y)^3 . if (25/36)^-3×(5/6)^-2=(x/y)^-8 ?​

Answer 1

Step-by-step explanation:

Given :-

(25/36)^-3×(5/6)^-2=(x/y)^-8

To find :-

Find the value of (x/y)^3 ?

Solution :-

Given equation is (25/36)^-3×(5/6)^-2=(x/y)^-8

=> [(5^2/6^2)^-3] × (5/6)^-2 = (x/y)^-8

=>[ (5/6)^2]^-3 × (5/6)^-2 = (x/y)^-8

Since (a/b)^m = a^m / b^m

=>[ (5/6)^(2×-3) ]×(5/6)^-2 = (x/y)^-8

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

=> (5/6)^-6 × (5/6)^-2 = (x/y)^-8

=> (5/6)^(-6)+(-2) = (x/y)^-8

Since a^m × a^n = a^(m+n)

=> (5/6)^(-6-2) = (x/y)^-8

=> (5/6)^-8 = (x/y)^-8

=> (x/y)^-8 = (5/6)^-8

On Comparing both sides then

=> x/y = 5/6

Therefore, the value of x/y = 5/6

Now, (x/y)^3 = (5/6)^3

=>(5/6)×(5/6)×(5/6)

=> (5×5×5)/(6×6×6)

=> 125/216

Answer:-

The value of (x/y)^3 for the given problem is 125/216

Used formulae:-

• a^m × a^n = a^(m+n)

• (a/b)^m = a^m / b^m

• (a^m)^n = a^(mn)

• If a^m = a^n => m = n