1.
To understand what it means to raise a number to the power of negative one, we first need to clarify the basic rules concerning exponents. When you raise a number to the power of a positive integer, you’re multiplying the number by itself as many times as the integer indicates. For example, 2^3 = 2 × 2 × 2 = 8.
So what happens when the exponent is negative? Here’s the essential rule: raising a number (let’s call it a) to the power of negative one, or a^(-1), equals the reciprocal of that number. Therefore, a^(-1) = 1/a. With that in mind:
1. Example: If we have the number 5, raising it to the power of negative one gives us:
5^(-1) = 1/5 = 0.2
2. Example: If we have the number 10, we can write:
10^(-1) = 1/10 = 0.1
3. Example: In the case of 0.25:
0.25^(-1) = 1/0.25 = 4
2. Conclusion At this point, you should have a clear understanding of what it means to raise a number to the power of negative one. It simply means taking the reciprocal of that number. It’s a fundamental concept that extends beyond just numbers; you’ll encounter this frequently in algebra, calculus, and other areas of mathematics. By grasping this principle, you can solve equations and inequalities involving negative exponents with ease!