Question

How do you simplify `-5^-2`?

Answer 1

`color(blue)(-1/25 or -0.04)`

Explanation:

`-5^-2`

since, `x^-1 = 1/x`,

therefore,

`1/-5^2`

= `1/(-(5)(5)`

= `-1/25`

Is the final answer :D

If the negative was meant to be part of the power, one would need to write `(-5)^-2`

Answer 2

`-0.04`

Explanation:

`-5^-2`

Remember `a^-n=1/(a^n)`

and that `-a=(-1)*a`

since the order of operations has us do powers before multiplication, the power does not affect the `-1`. The other way to look at it is that the power `5^-2` is being subtracted, in which case the order of operations also tells us to do the power before the subtraction:

`:.-5^-2=(-1)*1/(5)^2`

`=-1/((5)(5))`

`=-1/25=0.04`

If the negative was meant to be included in the power, it would need to be written as `(-5)^-2`