Question

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

Answer 1

1/4

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{$a^(-n)=\displaystyle(1)/(a^n)$}`

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

According to Property #7,

`\Large\text{2^(-2)=\displaystyle(1)/(2^2) =(1)/(4)$}`

Good luck with your studies.

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