>Hello Sohib EditorOnline! In this journal article, we will discuss how to calculate negative exponents, commonly known as “pangkat negatif” in Indonesian. Negative exponents can be tricky to understand at first, but with a bit of practice, you will be able to solve them with ease. Let’s get started!

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## What is a Negative Exponent?

A negative exponent is a shorthand way of writing a fraction with a 1 in the numerator and the base raised to the positive exponent in the denominator. For example, 2^-3 can be rewritten as 1/(2^3) or 1/8. In other words, a negative exponent indicates that the base should be divided by itself the number of times indicated by the exponent.

It is important to note that a negative exponent does not mean the answer is negative. The answer can be either positive or negative, depending on the base and the exponent.

## Rules for Calculating Negative Exponents

There are a few rules to follow when calculating negative exponents:

- Any number raised to the power of 0 is equal to 1. For example, 5^0 = 1.
- When multiplying numbers with the same base, add the exponents. For example, 2^3 x 2^2 = 2^5.
- When dividing numbers with the same base, subtract the exponents. For example, 2^5 / 2^3 = 2^2.
- When raising a power to another power, multiply the exponents. For example, (2^3)^2 = 2^6.
- When raising a fraction to a power, raise both the numerator and denominator to the power. For example, (1/2)^-3 = 2^3 / 1^3 = 8.

## Examples of Calculating Negative Exponents

Let’s look at some examples of how to calculate negative exponents:

Example | Calculation | Answer |
---|---|---|

2^-3 | 1/(2^3) | 1/8 |

5^-2 | 1/(5^2) | 1/25 |

(1/3)^-2 | (3/1)^2 | 9 |

4^-1 x 4^2 | 1/(4^1) x 4^2 | 16 |

10^-4 / 10^-2 | 10^2 / 10^4 | 1/100 |

## Frequently Asked Questions

### What is the difference between a negative exponent and a positive exponent?

A negative exponent indicates that the base should be divided by itself the number of times indicated by the exponent, while a positive exponent indicates that the base should be multiplied by itself the number of times indicated by the exponent.

### Can negative exponents be decimals or fractions?

Yes, negative exponents can be decimals or fractions. For example, 2^-0.5 is equal to 1/(2^0.5) or 1/(√2).

### Why are negative exponents important?

Negative exponents are important in many areas of mathematics and science, such as physics and engineering. They are also commonly used in algebraic expressions and equations.

### How can I check my answer for a negative exponent calculation?

You can check your answer by converting the negative exponent to a positive exponent and then evaluating the expression. For example, 2^-3 can be rewritten as 1/(2^3) or 1/8. To check your answer, you can evaluate 1/8 and see if it matches your original expression.

### What are some common mistakes when calculating negative exponents?

Some common mistakes include forgetting to convert the negative exponent to a positive exponent, confusing the rules for multiplying and dividing with the same base, and forgetting to apply the rule for raising a power to another power.

## Conclusion

Congratulations, Sohib EditorOnline! You now have a solid understanding of how to calculate negative exponents. Remember to follow the rules and practice with some examples to become comfortable with this concept. Good luck with your future calculations!