How do you simplify #2^0 - 2^-2#?

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Answer 1 · 2018-03-04T03:42:35

The result is #3/4#.

The definition of a negative exponent is as follows:

#quadcolor(red)a^-color(blue)xquad=>quad1/color(red)a^color(blue)x#

Also, anything to the power of #0# is #1#, so:

#quadcolor(blue)a^0=1#

Now, let's use these properties to simplify the expression:

#color(white)=color(red)(2^0)-color(blue)(2^-2)#

#=color(red)1-color(blue)(2^-2)#

#=color(red)1-color(blue)(1/2^2)#

#=color(red)1-color(blue)(1/4)#

#=color(red)(4/4)-color(blue)(1/4)#

#=color(purple)(3/4)#

That's the result. Hope this helped!