If n and k are positive integers and 8 to the power of n is equal to 2 to the power of k what is the value of n over k

8^n  =  2^k

Get the same base, turn  8  =  2³

Now, you can replace  8  with  2³  into the original formula:   ( 2³ ) ^ n  =  2 ^ k

If you have an exponent to an exponent, mutiply the exponents:  so,  ( 2³ ) ^ n  =  2 ^ (3n)

     2 ^ (3n)  =  2 ^ k             This will only be true if  3n  =  k

Since you want  n  over  k,  divide both sides by  k:  3n / k  =  k / k     --->  3n / k  =  1

Now, finish this by dividing both sides by 3     --->   n / k  =  1 / 3