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Why does a negative integer raised to an even power always result in a positive integer?
Wiki User
∙ 13y ago
The multiplication rule of thumb always states that a negative number times a negative number results in a positive number.
Since an even number is always divisible by two, any value raised to an even integer power will result in a positive number.
However, a basic proof is presented as follows:
(-A) * (-A) = A^2
((-A) * (-A)) ^ 2 = ((-A * -A) * (-A * -A)) = A^2 * A^2 = A ^ 4
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Wiki User
∙ 13y ago
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A negative number raised to an even power will be positive or negative?
Positive
Is -1 raised to the power of 100 negative or positive?
The answer is negative (-1 raised to the power of 100 = -1)
What is positive power and negative power?
x raised to a positive power, a is xa where a> 0. If a is an integer then it is equal to x*x*...*x where there are a lots of x.x raised to a negative power is the same as the reciprocal of x raised to the absolute value of the power. Thus, if b < 0 then xb = 1/x-bwhere -b > 0.x raised to rational or irrational powers are defined using the power laws.Another AnswerThe terms 'positive' and 'negative' powercan also be used to describe the direction of energy flow. For example, when a generator supplies energy to the grid, we can say that the direction of that energy and, therefore, the rate at which the energy flows (i.e. power) is positive. However, when the grid supplies energy back to the generator (causing it to 'motor'), then the energy (and, therefore, the power) is negative.
When a negative number is raised to an even power the result is a positive number?
Yes
16 to the negative 3 halves power Write with positive exponents and simplify show work t?
A base raised to a negative power is equal to 1 divided by that base raised to a positive exponent. So 16 raised to (-3/2) is equal to 1/ (16 raised 3/2), or 1/64.
Do a negative integer raised to an even power always results in a positive integer?
Yes.
Is a to the 3rd power greater than or equal to a for all integer values of A and why?
No. A negative integer raised to the third power will yield a negative number that is less than the integer. Only whole numbers (positive integers greater than or equal to 1) have the property where that integer raised to the third power is greater than or equal to the integer.
Why is any number raised to a even power positive?
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.
A negative number raised to an even power will be positive or negative?
Positive
Can you show me examples that a negative integer raised to an even power always results in an positive integer?
-32 this is like saying (-3)(-3) and a double negative is positive -34 this is like saying (-3)(-3)(-3)(-3) since there is two double negatives it is still positive -36 this is like saying (-3)(-3)(-3)(-3)(-3)(-3) since there is three double negatives it is still positive -38 this is like saying (-3)(-3)(-3)(-3)(-3)(-3)(-3)(-3) since there is four double negatives it is still positive This can apply for any negative integer.
When is a negative number raised to an odd power negative?
It is always negative when raised to an odd power and always positive when raised to an even power -2 to the third power = -2 x -2 x -2 = -8 -2 to the fourth power = -2 x -2 x -2 x -2 = +16
Is -1 raised to the power of 100 negative or positive?
The answer is negative (-1 raised to the power of 100 = -1)
What is the result of a negative number raised to the 54th power?
When a negative number is raised to an even power the result is a positive number
Is it true if a negative number is raised to the 18th power the answer will be negative?
No. Negative numbers to even powers are positive.
Is a negative number raised to an odd number always negative?
Yes.
Is a negative to a negative power 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.
When a number is raised to a power this number is multipled by itself the number of times the power indicates?
Yes (when the power is a positive integer). It is possible to have powers that are negative, rational, irrational and even complex and there are similar rules for dealing with them.
