State whether -4^-2 and (-4)^-2 represent the same quantity

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x^-2" just means "x2, but underneath, as in 1/x^2.

-4^-2 means the power -2 is only applied to 4 and not the negative sign. -4^-2 = -(4^-2), which is equal to -1/16.

Whereas, (-4)^-2 means the power -2 affects on both negative sign and 4. For example, (-4)^2 is equal to (-4 * -4) which is just 16. Moving on, with (-4)^-2 equals to 1/(-4*-4) = 1/16.

//Hope this helps.