Why does 2 to the negative 2 power equal 0.25?

Answer 1

A negative power simply means the base should be inverted. What does this mean? Well in simpler terms: the base is on the wrong side of the fraction line. So x^(-y) (that is: x to the power of negative y) is the same as 1/x^y (that is: one over x to the power of y) So 2^(-2) (two to the power of negative 2) is the same as 1/2^2 (that is: one over two to the power of negative 2) 2^2 = 4 , so 1/2^2 = 1/4 1/4 (one quarter) is 0.25. Why do negative exponents work this way? Well, think of it like this. When we multiply like bases: 5^7 x 5^2 we simply add the exponents: 5^7 x 5^2 = 5^9 similarly, if we divide like bases, we subtract the exponents: (5^7)/(5^2) = 5^5 but (5^7)/(5^2) is just another way of saying: (5^7) x (1/5^2) so we can just rewrite it: (5^7) x (5^-2) and then we add the exponents (5 + (-2)) and get 5^5 So negative exponents are a very simple way of showing information without writing a fraction.

Answer 2

When a number is raised to a negative exponent, it means the reciprocal of that number raised to the positive exponent. So, 2 to the negative 2 power is the same as 1 divided by 2 squared, which is 1 divided by 4, or 0.25. This is because raising a number to a negative exponent essentially flips the number to its reciprocal.

Answer 3

Oh, dude, it's like this - when you raise a number to a negative power, you're basically flipping it to its reciprocal. So, 2 to the negative 2 power is just 1 over 2 squared, which is 1 over 4, aka 0.25. It's math magic, but like, not that magical.

Answer 4

Well, when we have a negative exponent like -2, it means we need to take the reciprocal of the number raised to that power. So, 2 to the power of -2 is the same as 1 divided by 2 squared, which is 1 divided by 4, giving us 0.25. It's like a little math magic trick that helps us understand how numbers can work together in a beautiful way.

Answer 5

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Answer 6

Because it’s dividing by 2 then 2 again