**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`

.