Answer:
The value of k=1
So, Maura claim is incorrect. The value of k=1 and not k=1/2
Step-by-step explanation:
We need to determine the value of k if ![2^4=16^k](https://tex.z-dn.net/?f=2%5E4%3D16%5Ek)
We are given:
![2^4=16^k](https://tex.z-dn.net/?f=2%5E4%3D16%5Ek)
Exponent rule, if bases are equal the exponents are equal
We can write ![16= 2^4](https://tex.z-dn.net/?f=16%3D%202%5E4)
![2^4=(2^4)^k\\2^4=2^{4k}](https://tex.z-dn.net/?f=2%5E4%3D%282%5E4%29%5Ek%5C%5C2%5E4%3D2%5E%7B4k%7D)
Now since the base is same, i,e 2 so, the exponents will be same
![4=4k\\k=1](https://tex.z-dn.net/?f=4%3D4k%5C%5Ck%3D1)
So, the value of k=1
So, Maura claim is incorrect. The value of k=1 and not k=1/2