Negative indices (or exponents) represent the reciprocal of the base raised to the positive of that index. Simply put, a negative exponent means we need to take the reciprocal. For example, $x^{-n} = \frac{1}{x^n}$. Understanding this simple rule unlocks a whole new world of algebraic manipulations and problem-solving!
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Negative Index | A. The number that indicates how many times the base is multiplied by itself. |
| 2. Base | B. The number being raised to a power. |
| 3. Reciprocal | C. A power to which a base is raised that results in inverting the base. |
| 4. Exponent | D. Flipping a fraction, where the numerator becomes the denominator and vice versa. |
| 5. Power | E. The result of raising a base to an exponent. |
(Answers: 1-C, 2-B, 3-D, 4-A, 5-E)
Complete the following paragraph using the words provided: fraction, reciprocal, one, exponent, negative.
A _______ index tells us to take the _______ of the base. This means that $x^{-n}$ is the same as _______ over $x^n$. Therefore, negative exponents result in a _______. Also, the _______ becomes positive.
(Answers: negative, reciprocal, one, fraction, exponent)
Explain in your own words, why is it important to understand negative indices? Give one real-world example where negative indices might be used.
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