# What is 2 to the negative 2nd power?how did you get it?

bridgetrbcs | High School Teacher | (Level 2) Adjunct Educator

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In order to solve 2^-2, we must first look at negative powers.  Each time you have a negative power, the base of that power is moved to the other side of the fraction bar.

For example, if the number with the negative exponent is in the numerator (top) spot in the fraction, it will be moved to the denominator spot and the exponent will become positive.  However, if the number with the negative exponent is in the denominator (bottom) spot in the fraction, it will be moved to the numerator spot and the exponent will again become positive.

Now to specifically work your problem --  2^-2.  Because the base 2 is in the numerator spot we will move it to the denominator spot and make the -2 into a +2.

• 2^-2
• 1/(2^2)  Because there were no other numbers in this problem, we use the 1 as a place holder in the numerator spot after we move the 2 to the bottom.
• 1/4 Two squared is four.  It stays as the denominator and nothing needs to be done to the numerator since it does not have a power.

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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when you have a negative square you move the number with the square under one and get rid of the negative and then simply square it. in this case

2^-2= 1/2^2

=1/4

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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What is 2 to the negative 2nd power?

`2^-2`

Is the same as

`(1)/(2^2)`

according the laws of exponents.

The 1 in the numerator is just a place holder value since nothing else is there in this problem. Sometimes the numerator might have other terms to account for.

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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a negative exponent means the dot moves to the left and a positive exponent means the dot moves to the right. The spaces moved are converted into 0

2 ^-2 = .002

or you can just think of the exponents as the amount of zeroes behind 1, and the - and  + signs as divide and multiply signs

for example: ^-2 = a number divided by 100  (2 zeros)

^4 = a number multiplied by 10000