Which of the following powers do not have negative exponents?

The correct options are
C ${-1}^4$
D $5^2$

If the exponent of a power is a negative integer, then such a power is said to have negative exponent.

$a^m$ is said to be a power with negative exponent if a is any integer and m is any negative integer.

$-2^{-6}$ and $8^{-4}$ are powers with negative exponents -6 and -4 respectively, whereas $-1^4$ and $5^2$ are powers with positive exponents.