https://file.aiquickdraw.com/mathbot/file/1726322294966rg3uu9kr.jpg

The expression provided in the image can be interpreted as follows:

\[
\frac{x^{\frac{5}{4}} \cdot x^{-1}}{\sqrt[4]{x^3}}
\]

Now, let's break this down and simplify:

### Step 1: Simplifying the numerator
The numerator is \( x^{\frac{5}{4}} \cdot x^{-1} \).

Using the property of exponents \( x^a \cdot x^b = x^{a+b} \):

\[
x^{\frac{5}{4} + (-1)} = x^{\frac{5}{4} - \frac{4}{4}} = x^{\frac{1}{4}}
\]

So the numerator simplifies to \( x^{\frac{1}{4}} \).

### Step 2: Simplifying the denominator
The denominator is \( \sqrt[4]{x^3} \), which is equivalent to \( x^{\frac{3}{4}} \).

### Step 3: Putting it together
Now the entire expression becomes:

\[
\frac{x^{\frac{1}{4}}}{x^{\frac{3}{4}}}
\]

Using the exponent property \( \frac{x^a}{x^b} = x^{a-b} \):

\[
x^{\frac{1}{4} - \frac{3}{4}} = x^{-\frac{2}{4}} = x^{-\frac{1}{2}}
\]

### Final Answer:
The simplified expression is:

\[
x^{-\frac{1}{2}} = \frac{1}{\sqrt{x}}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the result change if the exponents in the numerator were different?
2. Can you simplify \( \frac{x^a}{x^b} \) for negative values of \( a \) and \( b \)?
3. How do fractional exponents relate to roots, and how can you convert between them?
4. What would the simplified expression be if the denominator was \( \sqrt[3]{x^5} \)?
5. How do exponent rules change when working with variables that involve constants, like \( 2^x \)?

**Tip:** Always remember to apply the properties of exponents carefully, especially when dealing with fractional and negative exponents.

Simplify the expression (x^(5/4) * x^(-1)) / (fourth root of x^3)

This tutorial explains how to simplify the algebraic expression involving fractional and negative exponents: (x^(5/4) * x^(-1)) / (fourth root of x^3). The step-by-step process includes exponent rules and key algebraic concepts, ideal for high school students (Grades 9-11).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation