https://file.aiquickdraw.com/mathbot/file/1727118483503m8ekuqxu.jpg

The expression shown in the image is:

\[
\left( z^{-1} \right) \left( \frac{x+1}{x+4} \right) \cdot \left( \frac{1}{y} \right)
\]

Let’s simplify this step-by-step:

1. The term \( z^{-1} \) is the same as \( \frac{1}{z} \).
2. Now we rewrite the expression as:
   \[
   \frac{1}{z} \cdot \frac{x+1}{x+4} \cdot \frac{1}{y}
   \]
3. Since we are multiplying fractions, we multiply the numerators and denominators together:
   \[
   \frac{(x+1)}{z \cdot y \cdot (x+4)}
   \]

So, the simplified form of the given expression is:
\[
\frac{x+1}{z y (x+4)}
\]

Would you like more details or clarifications on any part of this solution?

Here are some related questions:
1. How does exponentiation with negative exponents work?
2. What are the rules for multiplying fractions?
3. How can you apply these simplifications in complex rational expressions?
4. How would this expression change if \( z^{-1} \) was instead \( z^2 \)?
5. How can you evaluate this expression for specific values of \( x \), \( y \), and \( z \)?

**Tip**: Always rewrite negative exponents as fractions to make simplifications easier.

Simplify the following expression: z^(-1) * [(x + 1) / (x + 4)] * (1 / y)

Learn how to simplify the expression z^(-1) * (x + 1) / (x + 4) * (1 / y) step-by-step. This problem involves key algebraic concepts such as negative exponents and the multiplication of rational expressions. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation