Q: Will a negative number to the fifth power be a positive or negative value?

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It does not work that way. A negative power is simply the reciprocal. So that x-a = 1/xa The reciprocal is negative or positive according to whether the number itself is negative or positive. [And, if the number is 0, the reciprocal is not defined.]

Please consider the following two facts: A negative number to an even power is positive; but a negative number to an odd power is negative. Any positive number is greater than any negative number.

When a negative number is raised to an even power the result is a positive number

Yes. Any positive number to an exponent is positive.

No, or more accurately "not necessarily".A negative to any even power is positive. -2, -4, -6 etc. are even, so a negative number raised to any of those powers will be positive.However, a negative number raised to an odd negative power (-1, -3, -5 etc.) will be negative.

Related questions

negative

Negative, because 5 is an odd number

Positive

It does not work that way. A negative power is simply the reciprocal. So that x-a = 1/xa The reciprocal is negative or positive according to whether the number itself is negative or positive. [And, if the number is 0, the reciprocal is not defined.]

it is positive =1/25

Please consider the following two facts: A negative number to an even power is positive; but a negative number to an odd power is negative. Any positive number is greater than any negative number.

When a negative number is raised to an even power the result is a positive number

A positive number times a positive number is always positive. A negative number times a negative number is always positive. Therefore, any square number will be positive. Any number to the fourth power (a square times a square) will always be positive. And so on.

Yes. Any positive number to an exponent is positive.

A number to a negative power is equal to One divided by number to its positive power. So, x^-2 is equal to 1/x2.

1024 * * * * * That is 4 to the fifth power. The question asked about the NEGATIVE fifth power. For the question that was asked, the answer is 1/1024

Yes