Como Calcular Numero Elevado A Potencia Negativa
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Learn how to calculate a number raised to a negative exponent with our step-by-step guide and interactive calculator. Understand the mathematical rules, see practical examples, and avoid common pitfalls.
What is a negative exponent?
A negative exponent indicates the reciprocal of a number raised to a positive exponent. In mathematical terms, for any non-zero number a and positive integer n:
a⁻ⁿ = 1 / aⁿ
This means that a number with a negative exponent is equal to one divided by that number raised to the corresponding positive exponent. For example, 2⁻³ equals 1 divided by 2³, which is 1/8.
Remember that you cannot have a negative exponent with zero (0⁻ⁿ) because division by zero is undefined in mathematics.
How to calculate a number with a negative exponent
Calculating a number with a negative exponent follows these simple steps:
- Identify the base number and the exponent (including the negative sign).
- Convert the negative exponent to a positive exponent by moving the base to the denominator.
- Calculate the denominator by raising the base to the positive exponent.
- Simplify the fraction if possible.
Let's use the example of 5⁻²:
- Base is 5, exponent is -2.
- Convert to 1 / 5².
- Calculate 5² = 25.
- Final result is 1/25.
5⁻² = 1 / 5² = 1/25
Examples of negative exponents
Here are several examples to illustrate how negative exponents work:
| Expression | Calculation | Result |
|---|---|---|
| 3⁻¹ | 1 / 3¹ = 1/3 | 0.333... |
| 4⁻² | 1 / 4² = 1/16 | 0.0625 |
| 10⁻³ | 1 / 10³ = 1/1000 | 0.001 |
| (1/2)⁻⁴ | 1 / (1/2)⁴ = 2⁴ = 16 | 16 |
Notice how negative exponents with fractions work differently than with whole numbers. The negative exponent moves the fraction to the numerator.
Common mistakes with negative exponents
When working with negative exponents, it's easy to make these common errors:
- Forgetting to take the reciprocal: Some students mistakenly think a⁻ⁿ equals -aⁿ. Remember, the negative sign is only on the exponent, not the base.
- Applying the exponent to the negative sign: For example, thinking (-2)⁻³ equals -2³ instead of 1/(-2)³.
- Dividing by zero: Remember that 0⁻ⁿ is undefined because you can't divide by zero.
- Mixing up positive and negative exponents: Confusing a⁻ⁿ with aⁿ or a⁻ⁿ with 1/aⁿ.
Always double-check your work when dealing with negative exponents to ensure you've correctly converted them to positive exponents in the denominator.
FAQ
What does a negative exponent mean?
A negative exponent means you take the reciprocal of the base raised to the positive exponent. For example, 2⁻³ means 1 divided by 2³, which equals 1/8.
Can you have a negative exponent with zero?
No, you cannot have a negative exponent with zero because division by zero is undefined in mathematics. 0⁻ⁿ is not a valid expression.
How do you multiply numbers with negative exponents?
When multiplying numbers with the same base and negative exponents, you add the exponents. For example, a⁻² × a⁻³ = a⁻⁵. When the bases are different, you multiply the bases and add the exponents.
What happens when you raise a negative number to a negative exponent?
You take the reciprocal of the negative base raised to the positive exponent. For example, (-2)⁻³ equals 1 divided by (-2)³, which equals -1/8.