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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.
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ReneThat 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.
What does 10 to the negative 1 equal?
10 to the negative 1 is equal to 1 divided by 10, which simplifies to 0.1. This is because any number raised to the power of -1 is the reciprocal of that number. In this case, the reciprocal of 10 is 1/10 or 0.1.
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.
