The Value Of (0.6)^0 - (0.1)^-1

3 min read Jun 26, 2024
The Value Of (0.6)^0 - (0.1)^-1

The Value of (0.6)^0 - (0.1)^-1

In this article, we will explore the value of the expression (0.6)^0 - (0.1)^-1. To evaluate this expression, we need to understand the rules of exponents and how to apply them to decimal numbers.

Understanding Exponents

An exponent is a mathematical notation that represents repeated multiplication of a number by itself. For example, a^2 represents a multiplied by itself two times, or a × a. In general, a^n represents a multiplied by itself n times.

The Rule of Exponents: Any Number to the Power of 0

One important rule of exponents is that any number to the power of 0 is equal to 1. This means that:

a^0 = 1

This rule applies to all numbers, including decimal numbers.

Evaluating (0.6)^0

Using the rule of exponents, we can evaluate (0.6)^0 as follows:

(0.6)^0 = 1

The Rule of Exponents: Negative Exponents

Another important rule of exponents is that a number with a negative exponent is equal to the reciprocal of the number with a positive exponent. This means that:

a^-n = 1/a^n

Using this rule, we can evaluate (0.1)^-1 as follows:

(0.1)^-1 = 1/(0.1)^1 = 1/0.1 = 10

Evaluating (0.6)^0 - (0.1)^-1

Now that we have evaluated each part of the expression, we can combine them to get the final answer:

(0.6)^0 - (0.1)^-1 = 1 - 10 = -9

Therefore, the value of (0.6)^0 - (0.1)^-1 is -9.

Conclusion

In this article, we have explored the value of the expression (0.6)^0 - (0.1)^-1. By applying the rules of exponents, we were able to evaluate each part of the expression and combine them to get the final answer. The value of (0.6)^0 - (0.1)^-1 is -9.