## Mastering Lesson 4 Homework: Powers of Monomials Answer Key and Tips

### Introduction

Hello there, dear student! Are you having trouble with your lesson 4 homework on powers of monomials? Don’t worry, because you’re not alone. Simplifying monomial powers can be a challenging task for many of us. However, with proper understanding and practice, you can become a pro in no time! In this blog post, we’ll be discussing the answer key for the lesson 4 homework practice powers of monomials, as well as some useful tips and tricks to help you solve similar problems.

### Blog Body

#### Unraveling Monomial Powers: A Quick Review

Before we dive into the answer key, let’s have a quick review on what monomial powers are. A monomial is a polynomial with only one term, while monomial powers are the product of a monomial raised to a certain exponent. For instance, x^2 is a monomial power, where x is the base and 2 is the exponent. When simplifying monomial powers, we follow these basic rules:

- When multiplying monomial powers with the same base, we add their exponents. For example: x^2 * x^3 = x^(2+3) = x^5
- When dividing monomial powers with the same base, we subtract their exponents. For example: x^5 / x^2 = x^(5-2) = x^3
- When raising a monomial power to another exponent, we multiply their exponents. For example: (x^2)^3 = x^(2*3) = x^6

#### Navigating the Answer Key

With these rules in mind, let’s move on to the answer key for lesson 4 homework practice powers of monomials.

#### Problem-Solving with Answer Key

**Question 1:** Simplify 3x^2 * 2x^3 **Answer:** 6x^5 **Explanation:** We add the exponents of x to get the solution.

**Question 2:** Simplify 8x^2 / 2x **Answer:** 4x **Explanation:** We subtract the exponent of x in the denominator from the exponent of x in the numerator.

**Question 3:** Simplify (7x^3)^2 **Answer:** 49x^6 **Explanation:** We multiply the exponent of x by 2, which is the exponent outside the parentheses.

**Question 4:** Simplify 10x^4 / (5x^2) **Answer:** 2x^2 **Explanation:** We simplify by dividing 10/5 and subtracting the exponent of x in the denominator from the exponent of x in the numerator.

**Question 5:** Simplify (4x^2 y^3)^0 **Answer:** 1 **Explanation:** Any monomial raised to the exponent of zero is equal to 1.

### Conclusion

There you have it, dear student! With this guide on the answer key for lesson 4 homework practice powers of monomials, along with the basic rules on simplifying monomial powers, you’re now ready to tackle more complex problems with ease. Don’t forget to practice as much as you can, and always review your answers to identify your mistakes and learn from them. You got this!