Simplify.Assume j is greater than zero. sqrt ((7j^9)/(9)) square

To simplify the expression \(\sqrt{\frac{7j^9}{9}}\), we can follow these steps:<br /><br />1. **Separate the square root into two parts: the constant and the variable.**<br /> \[<br /> \sqrt{\frac{7j^9}{9}} = \sqrt{\frac{7}{9}} \cdot \sqrt{j^9}<br /> \]<br /><br />2. **Simplify the constants inside the square root.**<br /> \[<br /> \sqrt{\frac{7}{9}} = \sqrt{\frac{7}{3^2}} = \frac{\sqrt{7}}{3}<br /> \]<br /><br />3. **Simplify the variable part inside the square root.**<br /> \[<br /> \sqrt{j^9} = j^{9/2}<br /> \]<br /><br />4. **Combine the simplified parts.**<br /> \[<br /> \sqrt{\frac{7j^9}{9}} = \frac{\sqrt{7}}{3} \cdot j^{9/2}<br /> \]<br /><br />So, the simplified form of the given expression is:<br />\[<br />\boxed{\frac{\sqrt{7} \cdot j^{9/2}}{3}}<br />\]