Exponents are an important part of mathematics and can be used to simplify equations and solve problems. In lesson 6 of homework 3.7, students learn the basics of exponents and how they can be used. By the end of the lesson, students should be able to identify exponent terms, use the rules of exponents to simplify equations, and solve problems with exponents.

## What Are Exponents?

Exponents are mathematical symbols used to indicate the number of times a number should be multiplied by itself. For example, the number 2 with an exponent of 3 would be written as 2^{3} and would indicate that the number 2 should be multiplied by itself 3 times, or 2 x 2 x 2. This is also equivalent to 2 to the third power and can also be written as 2^3.

## Rules of Exponents

When working with exponents, there are several rules that should be followed. One of the most important rules is that when two exponents with the same base are multiplied together, the result is the same base with an exponent equal to the sum of the two original exponents. For example, if 2^{3} and 2^{2} were multiplied together, the result would be 2^{5}.

Another important rule to remember is that when an exponent is divided by another exponent with the same base, the result is the same base with an exponent equal to the difference of the two original exponents. For example, if 3^{4} is divided by 3^{2}, the result would be 3^{2}.

## Solving Problems with Exponents

Once students have a good understanding of the rules of exponents, they can begin to tackle problems involving exponents. To solve a problem with exponents, students should first identify any exponent terms in the problem and use the rules of exponents to simplify the equation. Once the equation is simplified, students can then solve the equation like any other algebra problem.

By the end of lesson 6 of homework 3.7, students should have a good understanding of exponents and how they can be used to simplify equations and solve problems. The rules of exponents are an important part of this understanding, and should be reviewed before attempting to solve any problems with exponents. With practice and dedication, students should be able to solve any problem involving exponents with ease.

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