Evaluate (5−7i)4(5−7𝑖)4 and leave your answer in polar form with the angle in degrees and all numbers rounded to the nearest whole number.

First, let's simplify the expression (5-7i)^4.

Step 1: Calculate the magnitude (r) and the angle (θ) of the complex number (5-7i). The magnitude r is given by √(a² + b²), where a and b are the real and imaginary parts of the complex number, respectively. So, r = √(5² + (-7)²) = √74 ≈ 9. The angle θ is given by arctan(b/a), so θ = arctan(-7/5) = -54 degrees.

Step 2: Convert the complex number to polar form. The polar form of a complex number is given by r(cos θ + i sin θ). So, (5-7i) = 9(cos(-54) + i sin(-54)).

Step 3: Raise the complex number to the power of 4. Using De Moivre's theorem, (r(cos θ + i sin θ))^n = r^n (cos(nθ) + i sin(nθ)). So, (5-7i)^4 = 9^4 (cos(4*-54) + i sin(4*-54)) = 6561(cos(-216) + i sin(-216)).

Step 4: Convert the result back to rectangular form. The rectangular form of a complex number is given by r cos θ + i r sin θ. So, (5-7i)^4 = 6561 cos(-216) + i 6561 sin(-216) = 6561(cos(-216) + i sin(-216)).

So, the result of (5-7i)^4 in polar form with the angle in degrees is 6561(cos(-216) + i sin(-216)).