Question

What is 2 to the power of -2? My teacher said it does not equal -4… does it equal positive 4??

Answer 1

Answer:

1/4

Step-by-step explanation:

2 to the power of -2 would be 1/4.

This is because 2 to the power of -1 would be 1/2. And the power of 2 would square the 2 as the denominator making it 1/4.

The reason -1 makes the 2 turn into a fraction is that to the power of 2 means 2x2, to the power of one means 2, The power of zero would therefore divide by 2 so 2/2 = 1 and so 2 to the power of -1 would be 1/2.

Answer 2

         $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

    What is 2 to the power of -2?

   $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

   

Let's look at the last property of exponents - $\bold{\#7 - negative\:exponents}$

                                    $\Large\text{ a^{-n}=\displaystyle\frac{1}{a^n} }$

So if we have a number with a negative exponent, we flip it over.

According to Property #7,

      $\Large\text{2^{-2}=\displaystyle\frac{1}{2^2} =\frac{1}{4} }$

Good luck with your studies.

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