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That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.
Consider this sequence:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 = 1/10
10-2 = 1/100
Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.
Consider this sequence:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 = 1/10
10-2 = 1/100
Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.
Consider this sequence:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 = 1/10
10-2 = 1/100
Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.
Consider this sequence:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 = 1/10
10-2 = 1/100
Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
That is the way it is defined; in theory, it could be defined any other way. But the definition commonly used makes several rules maintain their validity, for example, the law about adding exponents - even when the exponent is negative.
Consider this sequence:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 = 1/10
10-2 = 1/100
Every time the exponent is reduced by one, the result gets reduced by a factor of 10. So, it seems logical to continue this pattern for a zero or negative exponent. Mind you, this is no proof - after all, the negative exponents is a matter of definitions, not of proof. The above only merely shows that the definition is reasonable.
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Is a negative number raised to an odd power always negative?
Yes. Any multiplication involving an odd number of negative operands will be negative (assuming non-zero operands).
What is 5 to the power of negative 1?
When a number is raised to a negative exponent, it means the reciprocal of that number raised to the positive exponent. Therefore, 5 to the power of -1 is equal to 1/5, or 0.2. This is because any number raised to the power of -1 is the multiplicative inverse of that number, which is the reciprocal.
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 ...
What if raised to the power of one?
Any number raised to the power 1 is that same number, x1 = x. For example, 51 = 5.
What is 500000000 raised to the zero power?
Any number raised to the power of zero is just 1.
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.
What is negative 1 to the power of twenty?
-120= 1 because 1.) any negative number raised to an even power will result in a positive numberand 2.) 1 raised to any power is 1.
What is 1 to power of 10?
When a number is raised to the power of 1, the result is always the number itself. Therefore, 1 raised to the power of 10 is equal to 1. This is because any number raised to the power of 1 is simply the number itself, without any change.
Is a negative number raised to an odd power always negative?
Yes. Any multiplication involving an odd number of negative operands will be negative (assuming non-zero operands).
Log -3 equals?
There is no answer - it is an error: negative numbers do not have logarithms. The log if a number tells to what power the (positive) base must be raised to get the number. Raising any positive number to any power will never result in a negative number, so it is an error to try and take the log of a negative number.
What is 5 to the power of negative 1?
When a number is raised to a negative exponent, it means the reciprocal of that number raised to the positive exponent. Therefore, 5 to the power of -1 is equal to 1/5, or 0.2. This is because any number raised to the power of -1 is the multiplicative inverse of that number, which is the reciprocal.
What pattern do you discover when solving even-numbered exponents with negative bases?
Any number, positive or negative, raised to an even-numbered power, returns a positive number.
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.
What does 10 to the negative 73 power equal?
Any number x raised to a negative power -y is equivalent to the reciprocal of x raised to y. So, 10-73 would be the fraction 1 over the number 1 with 73 zeroes after it. A very small number indeed!
What is any number raised to the power of 1?
Any number raised to the power of 1 is the number itself. Example, 250 to the power of 1 is 250.
What is more than 25?
-- The sum of 25 and any positive number. -- The difference of 25 and any negative number. -- The product of 25 and any positive number greater than '1'. -- The ratio of 25 to any positive number less than '1'. -- 25 raised to any positive power greater than '1'. -- 25 raised to any negative power less than '1'. -- The factorial of any number greater than 5.
What does a number raised to the power of 1 equal?
Any number raised to the power of 1 is equal to itself.
