Simplify. \[ \frac{\sqrt{49 z^{15}}}{\sqrt{y^{7}}}= \]

Step 1 ：The given expression is a fraction of two square roots. To simplify this, we can use the property of square roots that the square root of a product is the product of the square roots. This means we can separate the square root of 49, the square root of \(z^{15}\), and the square root of \(y^{7}\).

Step 2 ：We can simplify the square root of 49 to 7, and the square root of \(z^{15}\) to \(z^{15/2}\). The square root of \(y^{7}\) can be simplified to \(y^{7/2}\).

Step 3 ：The final step is to write the simplified square roots as a fraction. So, the expression becomes \(7\sqrt{z^{15}}/\sqrt{y^{7}}\).

Step 4 ：The expression has been simplified, but it can be further simplified by expressing the square roots as powers of 1/2. So, the expression becomes \(7z^{15/2}/y^{7/2}\).

Step 5 ：The expression has been simplified to its final form, where the square roots are expressed as powers of 1/2.

Step 6 ：Final Answer: The simplified form of the given expression is \(\boxed{7z^{15/2}y^{-7/2}}\)