How to convert 010111 to decimal using only odd numbered positions while still applying the correct positional exponent?
I'm assuming positions are counted from $1$ starting from the least significant bit.

In this case you're using the exponents as if the number was 0111.
The question is asking to use the same exponents you would use for the odd-position digits of the number 010111.

To break it down, from the least to the most significant bit, the contribution to the final decimal value of each digit is:


First digit: $1 \cdot 2^0 = 1$.
Second digit: would be $1 \cdot 2^1 = 2$ but it is 0 since digits in even position are ignored.
Third digit: $1 \cdot 2^2 = 4$.
Fourth digit: ignored.
Fifth digit: $1 \cdot 2^4 = 16$.
Sixth digit: ignored.


The final result is: $16+4+1 = 21$.



Edit: Since you added that the answer should be $2$ this tells us that positions are either numbered starting from $0$, from the least to the most significant bit, or starting from $1$ from the most to the least significant bit.

In either case you would select the bits $001$ whose contribution would be $1 \cdot 2 + 0 \cdot 2^2 + 0 \cdot 2^4 = 2$.