\( 2 \sqrt[3]{7 x^{2}} \) and \( 8 \sqrt[3]{6 x^{2}} \)

It looks like you've provided two expressions involving cube roots: 1. \( 2 \sqrt[3]{7x^{2}} \) 2. \( 8 \sqrt[3]{6x^{2}} \) Let's explore how to simplify and potentially combine these expressions. ### Simplifying Each Expression 1. **First Expression:** \[ 2 \sqrt[3]{7x^{2}} \] This can be rewritten using exponent notation: \[ 2 \cdot 7^{1/3} \cdot x^{2/3} \] So, the simplified form is: \[ 2 \cdot 7^{1/3} \cdot x^{2/3} \] 2. **Second Expression:** \[ 8 \sqrt[3]{6x^{2}} \] Similarly, using exponent notation: \[ 8 \cdot 6^{1/3} \cdot x^{2/3} \] This can also be expressed by factoring out constants: \[ 2^3 \cdot 6^{1/3} \cdot x^{2/3} = 2 \cdot 2^2 \cdot 6^{1/3} \cdot x^{2/3} \] Simplifying further: \[ 8 \cdot 6^{1/3} \cdot x^{2/3} \] ### Combining the Expressions Both expressions share a common term \( x^{2/3} \). We can factor this out to combine the expressions: \[ 2 \cdot 7^{1/3} \cdot x^{2/3} + 8 \cdot 6^{1/3} \cdot x^{2/3} = x^{2/3} \left(2 \cdot 7^{1/3} + 8 \cdot 6^{1/3}\right) \] ### Final Simplified Form The combined expression is: \[ x^{2/3} \left(2 \cdot \sqrt[3]{7} + 8 \cdot \sqrt[3]{6}\right) \] This is as simplified as the expression can get unless there are specific values for \(x\) or further context provided. ### Summary - **Simplified First Expression:** \( 2 \cdot 7^{1/3} \cdot x^{2/3} \) - **Simplified Second Expression:** \( 8 \cdot 6^{1/3} \cdot x^{2/3} \) - **Combined Expression:** \( x^{2/3} \left(2 \cdot \sqrt[3]{7} + 8 \cdot \sqrt[3]{6}\right) \) If you have a specific operation in mind (like adding, subtracting, multiplying, etc.) or need further assistance with these expressions, feel free to provide more details!