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The solution to the equation \((5x - 7)^{\frac{2}{3}} - 6(5x - 7)^{-\frac{1}{3}} = 0\) is:

\[
x = 2.6
\]

Would you like more details or explanations on the steps? Here are five related questions that might deepen your understanding:

1. What is the meaning of fractional exponents like \( \frac{2}{3} \) or \( -\frac{1}{3} \) in this context?
2. How does one solve equations involving exponents and radicals?
3. Why do we use the property of exponents to simplify equations like this?
4. Can such equations have more than one solution in other cases?
5. What are the steps for verifying this solution?

**Tip:** When solving equations with fractional exponents, consider raising both sides to a power that eliminates the fraction. This helps simplify the equation.

Solve the following equation: (5x - 7)^(2/3) - 6(5x - 7)^(-1/3) = 0

Learn how to solve the equation (5x - 7)^(2/3) - 6(5x - 7)^(-1/3) = 0 step-by-step. This involves key algebraic concepts like fractional exponents and exponent rules. Suitable for students in Grades 10-12.

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