What is the value of 1 raised to a negative exponent? ... Maybe an example would help me better understand. Thank you very much ... I know it is like a fraction
1-1 = 1/11= 1
In fact, 1+345=1 and
1-345=1
zero to any power is 0
1 to any power is 1
Gotcha ... makes sense to me! :-) ... thank you! ... i may be back! :-)
To understand the value of 1 raised to a negative exponent, let's start with the definition of exponentiation. When a number is raised to an exponent, it means the number is multiplied by itself as many times as indicated by the exponent.
In this case, when we raise 1 to a negative exponent, such as 1 to the power of -3, it can be written as 1 / (1 * 1 * 1). So, let me explain this step-by-step:
1. Start with the base number, which is 1 in this case.
2. Write down the exponent, which is -3 in this example.
3. Rewrite 1 as a fraction with a numerator of 1 and a denominator of 1.
4. Since the exponent is negative, we need to take the reciprocal of 1. The reciprocal of 1 is still 1, so we don't need to change it in this case.
5. Now, we need to multiply 1 by itself for the number of times indicated by the absolute value of the exponent. In this case, the absolute value of -3 is 3, so we multiply 1 three times.
Here's how it looks: 1 / (1 * 1 * 1)
Simplifying further, we get: 1 / 1
Therefore, 1 raised to any negative exponent, in this case, -3, is equal to 1.
So, the value of 1 raised to a negative exponent is always 1.