Convert the point from rectangular coordinates into polar coordinates with $r\ge 0$ and $0\le \theta <2\pi$.
$$(7,-7)$$

Step 1 ：Given the rectangular coordinates of a point as (7,-7).

Step 2 ：We need to convert these rectangular coordinates into polar coordinates with $r\ge 0$ and $0\le \theta <2\pi$.

Step 3 ：The polar coordinates of a point in the plane are given by $(r,\theta )$ where $r$ is the distance of the point from the origin and $\theta$ is the angle the line joining the point to the origin makes with the positive x-axis.

Step 4 ：The conversion from rectangular coordinates $(x,y)$ to polar coordinates $(r,\theta )$ is given by: $$r=\sqrt{x^2+y^2}$$ and $$\theta =\arctan \left(\frac{y}{x}\right)$$.

Step 5 ：However, the $\arctan$ function only gives values in the range $(-\pi /2,\pi /2)$, so we need to adjust the value of $\theta$ depending on the quadrant of the point.

Step 6 ：If $x>0$ and $y\ge 0$, $\theta$ is in the correct range.

Step 7 ：If $x>0$ and $y<0$, we need to add $2\pi$ to $\theta$ to bring it into the range $(0,2\pi )$.

Step 8 ：If $x<0$, we need to add $\pi$ to $\theta$ to bring it into the correct range.

Step 9 ：If $x=0$ and $y>0$, $\theta =\pi /2$.

Step 10 ：If $x=0$ and $y<0$, $\theta =3\pi /2$.

Step 11 ：For the given point $(7,-7)$, we have $x=7$ and $y=-7$.

Step 12 ：Calculating $r$ using the formula, we get $r=\sqrt{7^2+(-7{)}^2}=9.899494936611665$.

Step 13 ：Calculating $\theta$ using the formula, we get $\theta =\arctan \left(\frac{-7}{7}\right)$. Since $x>0$ and $y<0$, we need to add $2\pi$ to $\theta$ to bring it into the range $(0,2\pi )$. So, $\theta =5.497787143782138$.

Step 14 ：$\boxed{{\displaystyle \text{Final Answer: The polar coordinates of the point }(7,-7)\text{ are }(9.899494936611665,5.497787143782138)}}$