How do you simplify 2^0 - 2^-22022?

1 Answer
Mar 4, 2018

The result is 3/434.

Explanation:

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!