Question

if (x/y) = (3/4) to the power 15 ÷(3/4) to the power 13 find the
value of (x/y) to the power -2
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Answer 1

Step-by-step explanation:

Given :-

x/y = (3/4)^15 ÷ (3/4)^13

To find :-

Find the value of (x/y)^-2?

Solution :-

Given that

x/y = (3/4)^15 ÷ (3/4)^13

=>x/y = (3/4)^15 / (3/4)^13

RHS is in the form of a^m / a^n

Where , a = 3/4 , m = 15 and n = 13

We know that

a^m / a^n = a^(m-n)

=> x/y = (3/4)^(15-13)

=> x/y = (3/4)^2

Now,

The value of (x/y)^-2

=> [(3/4)^2]^-2

This is in the form of (a^m)^n

Where , a = 3/4 , m = 2 and n = -2

We know that

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

=> [(3/4)^2]^-2

=> (3/4)^(2×-2)

=> (3/4)^-4

=> 1/(3/4)^4

Since a^-n = 1/a^n

=> (4/3)^4

=> (4×4×4×4)/(3×3×3×3)

=> 256/81

or

x/y = (3/4)^2

=> x/y = 9/16

Now,

The value of (x/y)^-2

=> (9/16)^-2

=> (16/9)^2

=> (16×16)/(9×9)

=> 256/81

Answer:-

The value of (x/y)^-2 is 256/81

Used formulae:-

• a^m / a^n = a^(m-n)
• a^-n = 1/a^n
• (a^m)^n = a^(mn)