### Introduction:

For students on the quest for an answer key to unravel the enigma of Lesson 18 Homework 5.4, you’ve stumbled upon the perfect destination. Math homework might seem like a maze, but fret not – we’re here to illuminate the path. In this blog, we’re breaking down every problem in this assignment, equipping you with step-by-step solutions to conquer mathematical challenges and excel in your class. So grab your pencil, settle in, and let’s embark on this mathematical journey!

### Problem 1: Decoding Exponents

**Solution:** First, let’s tackle the exponents. (-8)^2 equals 64, and (-8)^3 equals -512. Adding these values yields 64 + (-512), resulting in a solution of -448.

### Problem 2: Unraveling Algebraic Expressions

**Solution:** Begin by combining like terms. 18 + 4 equals 22, and -5x + 9x simplifies to 4x. Therefore, the simplified equation is 22 + 4x.

### Problem 3: Unveiling Rectangle Dimensions

**Solution:** Let’s denote the width as x. The length becomes x + 5. The perimeter formula is 2(length + width), leading to the equation 2(x + 5 + x) = 86. Simplifying yields 4x + 10 = 86, and further simplification gives 4x = 76. Thus, x equals 19. The width is 19 cm, and the length is 24 cm.

### Problem 4: Solving Algebraic Equations

**Solution:** Distribute the 4 on the left side to get 4x + 4 – 2 = 14 – 2x. Simplifying leads to 6x = 12, and solving for x yields x = 2.

### Problem 5: Navigating Compound Interest

**Solution:** Employ the formula A = P(1 + r/n)^(nt). With A as $3500, P as $3000, r as 0.06 (6% expressed as a decimal), n as 1, and x as the unknown number of years, the equation becomes 3500 = 3000(1 + 0.06/1)^(1x). Simplifying and solving for x yields x = 3.86 years.

### Conclusion:

Having traversed each problem within Lesson 18 Homework 5.4, you should now possess a firmer grasp of the concepts and the ability to tackle analogous problems in the future. Remember, practice hones perfection, so persist in your endeavors and seek assistance when challenges arise. While math homework may seem intricate, armed with the right tools and mindset, you possess the prowess to decipher its intricacies and triumph. Your mathematical journey is one of discovery and mastery – embrace it with confidence and stride forward toward success!