Solve the given equation 3=(7^(1)/(3))(x^(1)/(3)) x=square (Type an integer or a simplified fraction.)

To solve the equation \(3 = (7^{\frac{1}{3}})(x^{\frac{1}{3}})\), we need to isolate \(x\). Here are the steps:<br /><br />1. Start with the given equation:<br /> \[<br /> 3 = (7^{\frac{1}{3}})(x^{\frac{1}{3}})<br /> \]<br /><br />2. Rewrite the equation to separate the cube roots:<br /> \[<br /> 3 = 7^{\frac{1}{3}} \cdot x^{\frac{1}{3}}<br /> \]<br /><br />3. To eliminate the cube roots, raise both sides of the equation to the power of 3:<br /> \[<br /> (3)^3 = (7^{\frac{1}{3}} \cdot x^{\frac{1}{3}})^3<br /> \]<br /><br />4. Simplify both sides:<br /> \[<br /> 27 = 7 \cdot x<br /> \]<br /><br />5. Solve for \(x\) by dividing both sides by 7:<br /> \[<br /> x = \frac{27}{7}<br /> \]<br /><br />So, the solution to the equation is:<br />\[<br />x = \frac{27}{7}<br />\]