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They are not! 5-3, for example is not 1/52 nor (1/5)2.

Q: Why are 5 to the negative power and 1 over 5 to the 2 power the same?

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That is the definition of negative powers.

It is 1 over that number to the same power, but positive. So 4^-5=1/4^5

It is equivalent to 1 over 5 to the power of 5, or 1 over 3125.

Yes.

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That is the definition of negative powers.

it's the same as 1 over the same number to a positive power. 2 to the power -3 = 1/ 2 cubed = 1/8

It is 1 over that number to the same power, but positive. So 4^-5=1/4^5

1 over 3 to the negative 2nd power is 9

It is equivalent to 1 over 5 to the power of 5, or 1 over 3125.

Yes.

1-1 is the same as 1/1 = 1

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1000000 * * * * * NO! That is 10 to the power of 6. 10 to the power of NEGATIVE 6 is 1 over 1000000 or 0.000001

It's the inverse of the number raised to the power. 2 to the power of negative 3 would be 1/8th.1 over 25Improvement(shininggallade):When raising a whole number to a negative power, simply raise 5 to the second power, which is 25, and put a 1 over it. 5^-2=1/25 A more technical definition is to reverse the numerator and denominator and then apply the power. Remember 5 is the same as 5/1, so (5^-2)/1=1/(5^2)=1/25(The symbol for "to the power of" is "^" just to let you know.)

it is a positive fraction 5^-2=1 over 5^2 answer is 1 over 25

That is the same as 1 divided by 8 to the positive power 1/(8x8x8) = 1/512