Table of Contents

## An Introduction to Exponents

- An exponent is a number that indicates how many times a number is to be multiplied by itself. The number that is multiplied is called the base, and the number that indicates how many times to multiply the base is the exponent.
- For example, the number 5 has an exponent of 1 because it is multiplied by itself once, or 5 * 5 = 25. The number 64 has an exponent of 2 because it is multiplied by itself twice, or 64 * 64 = 4096.
- The number 3.14 has an exponent of 0 because it is not multiplied by itself.
- The base number can be any number, including decimals and fractions.
- When a number is raised to an exponent, the result is called a power. For example, 5 raised to the power of 2 is 25, because 5 multiplied by itself 2 times is 25.

The following are some basic exponent rules:

1. Any number raised to the power of 0 is 1. For example, 5 raised to the power of 0 is 1.

2. Any number raised to the power of 1 is the number itself. For example, 5 raised to the power of 1 is 5.

3. Any number raised to the power of a negative number is equal to 1 divided by the number raised to the power of the positive number. For example, -5 raised to the power of 3 is equal to 1 divided by 5 raised to the power of 3,

## Defining What Exponents Mean

An exponent is a number that is written as a superscript following the base number in a mathematical equation. The exponent indicates how many times the base number should be multiplied by itself. For example, the equation 2^3 means 2 multiplied by itself 3 times, or 2x2x2. The result of this equation is 8.

## A Gist about Negative Numbers with Examples

- Negative numbers are numbers that are less than zero. They are typically represented by a minus sign (-) before the number.
- Some examples of negative numbers include -3, -5, and -8.
- Negative numbers can be used in a variety of ways. For instance, they can be used to represent debts or negative temperatures. Additionally, they can be used in mathematical equations to help solve problems.

## Rules of Exponents

- When multiplying or dividing powers with the same base, add or subtract the exponents.
- When adding or subtracting powers with the same base, keep the base and add or subtract the exponents.
- When raising a power to a power, multiply the exponents.

## Negative Exponents

- A negative exponent is a number that is preceded by a minus sign (ˇ). It is used to indicate that a number is to be divided by a certain power of 10.
- For example, the number 0.0000001 can be written as ˇ-7. This means that the number is to be divided by 107.

## Fractional Exponents

A fractional exponent is a number that is represented as a fraction and is used to indicate a root. The number inside the parentheses is the root that is being taken and the number outside of the parentheses is the power.

## Importance of Exponents

- The importance of exponents comes from the fact that they allow for the efficient description of certain relationships. In mathematics, an exponent is a number that indicates how many times a number is to be multiplied by itself. For instance, in the expression 3^2, the 3 is the base number and the 2 is the exponent. This expression means that the base number is multiplied by itself two times. The result is 9.
- When dealing with large numbers, exponents can be used to shorten long multiplication problems. For instance, the number 1,000,000 can be written as 106. This is because 1,000,000 is equal to 1 multiplied by 1,000,000 times 10, which is written as 106. This is because the number 10 has a value of 1,000.
- Exponents can also be used to describe the relationship between two or more numbers. In the expression 2^3, the 2 is the base number and the 3 is the exponent. This expression means that the base number is multiplied by itself three times. The result is 8.
- The importance of exponents comes from the fact that they allow for the efficient description of certain relationships. In mathematics, an exponent is a number that indicates how many times a number is to be multiplied by itself. For instance, in the expression 3^2, the 3 is the base number and the 2 is the exponent. This expression means that the base number is multiplied by itself two times