Final answer:
To find the value of y, we simplified the equation using exponent properties, resulting in y = 14. However, this answer does not match any of the provided options, suggesting an error in the question or options.
Step-by-step explanation:
To find the value of y in the equation 2^4 * 2^y = (2^3)^6, we need to use the properties of exponents to simplify the equation.
To simplify the left side of the equation, we use the property that when we multiply powers with the same base, we can add the exponents: 2^4 * 2^y = 2^(4+y).
On the right side, the property that when we raise a power to a power, we multiply the exponents is used: (2^3)^6 = 2^(3*6) = 2^18.
Now the equation is 2^(4+y) = 2^18. Since the bases are the same and the powers must be equal, we can set the exponents equal to each other: 4 + y = 18. Solving for y, we subtract 4 from both sides to get y = 18 - 4 = 14.
However, none of the given options matches our calculation. There might be an error in the question or in the options provided. The correct value we found is y = 14, which is not listed as an option.