https://file.aiquickdraw.com/mathbot/file/17255183948169kerqta0.jpg

The image you uploaded contains a complex algebraic expression. I'll break it down and help simplify the expression.

The expression is:

\[
\frac{(4x^3y^{-2})^{-\frac{1}{7}}(16x^{-4}y^6)^{\frac{3}{7}}}{\left( \frac{64x^{-6}y^8}{x^3} \right)^{\frac{1}{3}}}
\]

Let me simplify this step-by-step.The simplified form of the expression is:

\[
0.673 \cdot \left(\frac{y^6}{x^4}\right)^{\frac{3}{7}} \cdot \left(\frac{y^8}{x^9}\right)^{-\frac{1}{3}} \cdot \left(\frac{x^3}{y^2}\right)^{-\frac{1}{7}}
\]

If you'd like, I can further simplify this or explain the steps in more detail. Let me know if you need further clarification!

Here are five related questions for deeper exploration:

1. How do you simplify expressions involving negative exponents?
2. What are the steps to solve expressions with fractional exponents?
3. How can you factor expressions with multiple variables?
4. What are the properties of exponents used in simplifying algebraic expressions?
5. How can you apply exponent rules when simplifying large expressions?

**Tip:** When working with fractional and negative exponents, always try to rewrite them in terms of positive exponents and fractions for easier manipulation.

Simplify the algebraic expression involving exponents and fractional powers.

Learn how to simplify a complex algebraic expression with fractional and negative exponents. This problem involves the use of exponent rules to simplify powers of variables. Suitable for students in Grades 10-12.

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