Base in the expression 1024 is 24.

Explanation:

In the number system, the base is the number of digits or values used to represent a number. For example, in the decimal number system, the base is 10, as there are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) used to represent any number.

In the given expression 1024, the number is written in the base 10 system. However, if we convert this number to the base 2 system (binary), we get:

1024 = 2^10

Therefore, the base in the expression 1024 is 2, as the number can be written as a power of 2 raised to the 10th power.

However, if we consider the number 1024 in the hexadecimal (base 16) system, we can write:

1024 = 4 x 16^2

Therefore, the base in the expression 1024 is 16, as the number can be written as a product of 4 and 16 raised to the 2nd power.

Similarly, if we consider the number 1024 in the octal (base 8) system, we can write:

1024 = 2^12

Therefore, the base in the expression 1024 is 8, as the number can be written as a power of 8 raised to the 12th power.

Hence, the base in the expression 1024 depends on the number system in which it is represented. In the given expression, the number is represented in the decimal system, and if we write it in terms of powers of 2, the base is 24.

Answer is b not d. Base is 10 and exponent or power is 24.