Final answer:
None of the provided options are correct. To solve for n in the equation 2^2×2^n=(2^4)^3, we simplify and equate the exponents since the bases are the same, resulting in n = 10. However, this solution does not match any of the given options, indicating an error in the question.
Step-by-step explanation:
To find the value of n in the equation 2^2×2^n=(2^4)^3, let's simplify both sides of the equation using the rules of exponents.
On the left-hand side:
2^2×2^n = 2^(2+n)
On the right-hand side:
(2^4)^3 = 2^(4×3)
2^(4×3) = 2^12
Now we have 2^(2+n) = 2^12. Since the bases are the same, we can equate the exponents:
2+n = 12
Solving for n:
n = 12 - 2
n = 10
Therefore, the value of n is 10, which is not listed in the given options (a) 2, (b) 3, (c) 4, and (d) 5. There seems to be an error in the question as none of the provided options are correct.