https://r2.erweima.ai/mathbot/image/1725551476990lvkajgrx.jpg

The expression shown in the image is:

\[
x^{-\frac{4}{3}} - x^{-\frac{7}{3}} + x^{-\frac{2}{3}}
\]

### Factoring Process:

1. Identify the lowest power of \(x\) among the terms: 
   - The exponents are \(-\frac{4}{3}, -\frac{7}{3},\) and \(-\frac{2}{3}\).
   - The lowest exponent is \( -\frac{7}{3} \).

2. Factor out \(x^{-\frac{7}{3}}\) from all the terms:

\[
x^{-\frac{7}{3}} \left( x^{\frac{3}{3}} - 1 + x^{\frac{5}{3}} \right)
\]

3. Simplify the exponents:
   \[
x^{-\frac{7}{3}} \left( x^1 - 1 + x^{\frac{5}{3}} \right)
\]

Thus, the factored form of the expression is:

\[
x^{-\frac{7}{3}} \left( x - 1 + x^{\frac{5}{3}} \right)
\]

Would you like further clarification or details on any step? 

Here are 5 related questions to explore further:

1. How can you identify the greatest common factor in algebraic expressions?
2. What are the rules for factoring expressions with fractional exponents?
3. How do negative exponents affect the factoring process?
4. How can we simplify expressions with different powers of \(x\)?
5. What is the importance of recognizing patterns in exponents during factoring?

**Tip:** When factoring, always check for the lowest power of the variable first, as this simplifies the expression.

Factor the expression by factoring out the lowest power of each common factor: x^(-4/3) - x^(-7/3) + x^(-2/3).

Learn how to factor expressions with negative exponents by factoring out the lowest power. This detailed solution walks through the factoring process for x^(-4/3) - x^(-7/3) + x^(-2/3), applying exponent rules and simplification techniques. Suitable for Grades 9-12.

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