(3)/(sqrt [3](2x))+(3)/(sqrt [3](7x))

To simplify the expression \(\frac{3}{\sqrt[3]{2x}} + \frac{3}{\sqrt[3]{7x}}\), we can follow these steps:<br /><br />1. **Rewrite the cube roots in exponential form:**<br /> \[<br /> \sqrt[3]{2x} = (2x)^{1/3} \quad \text{and} \quad \sqrt[3]{7x} = (7x)^{1/3}<br /> \]<br /><br />2. **Express the given expression using these forms:**<br /> \[<br /> \frac{3}{(2x)^{1/3}} + \frac{3}{(7x)^{1/3}}<br /> \]<br /><br />3. **Factor out the common factor of 3:**<br /> \[<br /> 3 \left( \frac{1}{(2x)^{1/3}} + \frac{1}{(7x)^{1/3}} \right)<br /> \]<br /><br />4. **Combine the terms inside the parentheses:**<br /> \[<br /> 3 \left( \frac{(7x)^{1/3} + (2x)^{1/3}}{(2x)^{1/3} (7x)^{1/3}} \right)<br /> \]<br /><br />5. **Simplify the denominator:**<br /> \[<br /> (2x)^{1/3} (7x)^{1/3} = (2x \cdot 7x)^{1/3} = 14x^{1/3}<br /> \]<br /><br />6. **Combine the numerator and denominator:**<br /> \[<br /> 3 \left( \frac{(7x)^{1/3} + (2x)^{1/3}}{14x^{1/3}} \right)<br /> \]<br /><br />7. **Simplify the fraction:**<br /> \[<br /> 3 \left( \frac{(7x)^{1/3} + (2x)^{1/3}}{14x^{1/3}} \right) = \frac{3}{14x^{1/3}} \left( (7x)^{1/3} + (2x)^{1/3} \right)<br /> \]<br /><br />So, the simplified form of the given expression is:<br />\[<br />\boxed{\frac{3}{14x^{1/3}} \left( (7x)^{1/3} + (2x)^{1/3} \right)}<br />\]