What is the value of $K$ in the equation $16^3\times8^3=2^K$?
We can write $16^3$ as $(2^4)^3=2^{12}$. That's correct. $16$ is $2$ to the fourth power. And since we have it to the third power, we can rewrite it as $2^{12}$. Right. We can also rewrite $8^3$ as $(2^3)^3$ which is $2^9$. So now we have $2^{12} * 2^9 = 2^K$. That's correct. And since $2^{12} * 2^9 = 2^{21}$, we know $K$ must be equal to $21$. So the value of $K$ in the equation $2^{12} * 2^9 = 2^K$ is $21$.

