https://file.aiquickdraw.com/mathbot/file/1725372833516jpavmfl3.jpg

The equation in the image is:

\[
T^3 = \sqrt{A \times B^{2/3} + C^{3/4}}
\]

Here's a breakdown of the equation:

1. **Left-hand side (LHS):** \( T^3 \) represents \( T \) raised to the power of 3.
2. **Right-hand side (RHS):** The square root of the expression \( A \times B^{2/3} + C^{3/4} \).

### Steps to Solve for \( T \):

1. **Isolate the square root:**
   \[
   T^3 = \sqrt{A \times B^{2/3} + C^{3/4}}
   \]
   
2. **Remove the square root by squaring both sides:**
   \[
   T^6 = A \times B^{2/3} + C^{3/4}
   \]
   
3. **Solve for \( T \):**
   \[
   T = \left(A \times B^{2/3} + C^{3/4}\right)^{1/6}
   \]

This expression gives you \( T \) in terms of \( A \), \( B \), and \( C \).

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

Here are some related questions:
1. How do we simplify expressions involving fractional exponents?
2. What is the general method for solving equations involving radicals?
3. How does squaring both sides of an equation affect the solution?
4. What are potential pitfalls when dealing with square roots and even powers?
5. How can you apply this method to more complex algebraic equations?

**Tip:** When dealing with equations involving radicals, always check for extraneous solutions that may arise when squaring both sides of the equation.

Solve for T given the equation T^3 = √(A × B^(2/3) + C^(3/4))

Learn how to solve the equation T^3 = √(A × B^(2/3) + C^(3/4)) step-by-step. This problem covers algebraic concepts like radicals and fractional exponents, suitable for students in Grades 9-11.

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