Question

2^12÷2^(k/2 )= 32 find k​

Answer 1

k = 14

Explanation:

Prime factorize 32

32 = 2 * 2 * 2 * 2 * 2 = 2⁵

`\frac{2^(12)}{2^{(k)/(2)}}= 32\\\\\frac{2^(12)}{2^{(k)/(2)}}=2^(5)\\\\2^{12-(k)/(2)}=2^(5)`

Both sides base are same.So, compare exponents

`12-(k)/(2)=5\\`

Subtract 12 from both side

`-(k)/(2)=5-12\\\\-(k)/(2)=-7\\`

Multiply both sides by (-2),

`(-2)*(-(k)/(2))=-7*(-2)\\\\k = 14`