### Instruction: What is the value of $K$ in the equation $16^3\times8^3=2^K$?### Response: I notice that all the bases in this equation are powers of 2, so I can rewrite them as such.
16 is 2 to the fourth power, so 16 cubed is 2 to the 12th power.
8 is 2 to the third power, so 8 cubed is 2 to the ninth power.
Multiplying powers with the same base means adding their exponents, so 16 cubed times 8 cubed is 2 to the 21st power.
That means 2 to the 21st power is equal to 2 to the Kth power, and the only way that can be true is if K is also 21.