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

Answer 1

Isaiah Anthony

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!

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Answer 2

Eva Adamson

To simplify ( 2^0 - 2^{-2} ), we use the properties of exponents. ( 2^0 = 1 ) because any number raised to the power of 0 equals 1. ( 2^{-2} ) is the same as ( \frac{1}{2^2} = \frac{1}{4} ). Therefore, ( 2^0 - 2^{-2} = 1 - \frac{1}{4} = \frac{3}{4} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.