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You can understand this by using one rule of exponents. For integers m,n, and positive integer a a^m/a^n=a^(m-n) So if we look at a^m/a^m which must be 1 since it is something divided by itself, we know from the rule we can also write this as a^(n-n)=a^0 but we just showed that was 1.

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โˆ™ 2008-11-16 04:14:49
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Q: When a positive integer is raised to the power of zero the answer is always one. Why?
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Related questions

Do a negative integer raised to an even power always results in a positive integer?

Yes.


Why does a negative integer raised to an even power always result in a positive integer?

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 ...


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.


How much is any integer raised to the zero power?

Any integer raised to the power of zero is 1.


What is the forth powerof a positive integer?

let x be any positive integer then x4 is the 4th power of that positive 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.


Why are the units digit of any positive integer power of 5 will always be 5?

The units digit of any number is the number in the ones position. For example, the units digit of 123 is 3; 2324 is 4; and 87321 is one. The reason the answer is 5 for 5 raised to any positive integer is because 5 will always be in the units position. For example, 52 = 25; 53 = 125; 54 = 625; and so on.


What is negative integer to the tenth power?

It will be the same as its positive counterpart to the tenth power.


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.


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 it possible for a large prime number to be expressed as a large integer raised to a very large power?

No. Any number raised to a power is not prime.


What is a rule for raising a negative number to a power?

It is the positive form of the number raised to that power, multpilied by -1 raised to that power.


Is -1 raised to the power of 100 negative or positive?

The answer is negative (-1 raised to the power of 100 = -1)


A negative number raised to an even power will be positive or negative?

Positive


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


When will you say that Algebraic Expression is not Polynomial?

When it has any term in which the variable is not raised to a non-nagative integer power. So for example, if it contains a term such as x-3 [the power is not positive] or x1/2 or sqrt(x) [the power is not an integer] or sin(x), or log(x) etc [not powers of x].


Is any number raised to a even power positive?

yes


What is 11000 to the power 0?

Any positive non-zero integer to the power zero is equal to 1.


Why doesnt the function y ex ever cross the x-axis?

no number can be raised to a power and equal 0 (x^y can never = 0). e is positive (about 2.7) and any positive number can not be raised to a power and equal negative (positive number X positive number = positive number)


What does any nonzero raised to the zero power equal?

Any number raised to the power of zero is always equal to 1


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.


Which number is equivalent to the power of 10?

A positive integer power of ten is of the form 1 followed by zeros: ten, hundred, billion and so on.A fractional power of ten can be any positive number - the logarithm (to base 10).A positive integer power of ten is of the form 1 followed by zeros: ten, hundred, billion and so on.A fractional power of ten can be any positive number - the logarithm (to base 10).A positive integer power of ten is of the form 1 followed by zeros: ten, hundred, billion and so on.A fractional power of ten can be any positive number - the logarithm (to base 10).A positive integer power of ten is of the form 1 followed by zeros: ten, hundred, billion and so on.A fractional power of ten can be any positive number - the logarithm (to base 10).


Is -7 raised to the power of 3 equals to -7 raised to the power of 3?

Reflexivity is a property of equality, i.e., X = X is always true. Thus -7 raised to the power of 3 equals -7 raised to the power of 3 is true.


Is it possible for an extremely large prime to be expressed as a large integer raised to a very large power why or why not?

ne


What is the value of any nonzero base raised to the zero power?

The value of any nonzero number raised to the zero power will equal positive one (1).