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

2 Answers
Mar 10, 2016

Answer:

#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:

#-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#