Question

 If 2^(m+n) / 2^(n - m) = 16, then m is ​

Answer 1

Step-by-step explanation:

answer will be 2 ..

I hope it will be helpful for you

Answer 2

Step-by-step explanation:

Given :-

2^(m+n) / 2^(n - m) = 16

To find :-

Find the value of m ?

Solution :-

Given that :

2^(m+n) / 2^(n - m) = 16

We know that

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

=> 2^[(m+n)-(n-m] = 16

=> 2^(m+n-n+m) = 16

=> 2^(m+m) = 16

=> 2^(2m) = 16

=> 2^(2m) = 2^4

Since (16=2×2×2×2)

We know that

If bases are equal then exponents must be equal

=> 2m = 4

=> m = 4/2

=> m = 2

Therefore, the value of m = 2

Answer:-

The value of m for the given problem is 2

Check :-

If m = 2 then LHS in the given equation

2^(m+n) / 2^(n - m)

=>2^(2+n)/2^(n-2)

=> 2^[(2+n)-(n-2)]

=> 2^(2+n-n+2)

=> 2^(2+2)

=> 2^4

=> 2×2×2×2

=> 16

=> RHS

LHS = RHS is true for m = 2

Used formulae:-

• a^m / a^n = a^(m-n)

• If bases are equal then exponents must be equal

• If a^m = a^n => m = n