x = -(-30/7)^(1/25) or x = (30/7)^(1/25) or x = (-1)^(2/25) (30/7)^(1/25) or x = -(-1)^(3/25) (30/7)^(1/25) or x = (-1)^(4/25) (30/7)^(1/25) or x = -(-1)^(1/5) (30/7)^(1/25) or x = (-1)^(6/25) (30/7)^(1/25) or x = -(-1)^(7/25) (30/7)^(1/25) or x = (-1)^(8/25) (30/7)^(1/25) or x = -(-1)^(9/25) (30/7)^(1/25) or x = (-1)^(2/5) (30/7)^(1/25) or x = -(-1)^(11/25) (30/7)^(1/25) or x = (-1)^(12/25) (30/7)^(1/25) or x = -(-1)^(13/25) (30/7)^(1/25) or x = (-1)^(14/25) (30/7)^(1/25) or x = -(-1)^(3/5) (30/7)^(1/25) or x = (-1)^(16/25) (30/7)^(1/25) or x = -(-1)^(17/25) (30/7)^(1/25) or x = (-1)^(18/25) (30/7)^(1/25) or x = -(-1)^(19/25) (30/7)^(1/25) or x = (-1)^(4/5) (30/7)^(1/25) or x = -(-1)^(21/25) (30/7)^(1/25) or x = (-1)^(22/25) (30/7)^(1/25) or x = -(-1)^(23/25) (30/7)^(1/25) or x = (-1)^(24/25) (30/7)^(1/25)
Step-by-step explanation:
Solve for x:
7 x^25 = 30
Hint: | Divide by an appropriate factor to make the coefficient of x^25 equal to 1.
Divide both sides by 7:
x^25 = 30/7
Hint: | Take 25^th roots of both sides.
Taking 25^th roots gives (30/7)^(1/25) times the 25^th roots of unity:
Answer: x = -(-30/7)^(1/25) or x = (30/7)^(1/25) or x = (-1)^(2/25) (30/7)^(1/25) or x = -(-1)^(3/25) (30/7)^(1/25) or x = (-1)^(4/25) (30/7)^(1/25) or x = -(-1)^(1/5) (30/7)^(1/25) or x = (-1)^(6/25) (30/7)^(1/25) or x = -(-1)^(7/25) (30/7)^(1/25) or x = (-1)^(8/25) (30/7)^(1/25) or x = -(-1)^(9/25) (30/7)^(1/25) or x = (-1)^(2/5) (30/7)^(1/25) or x = -(-1)^(11/25) (30/7)^(1/25) or x = (-1)^(12/25) (30/7)^(1/25) or x = -(-1)^(13/25) (30/7)^(1/25) or x = (-1)^(14/25) (30/7)^(1/25) or x = -(-1)^(3/5) (30/7)^(1/25) or x = (-1)^(16/25) (30/7)^(1/25) or x = -(-1)^(17/25) (30/7)^(1/25) or x = (-1)^(18/25) (30/7)^(1/25) or x = -(-1)^(19/25) (30/7)^(1/25) or x = (-1)^(4/5) (30/7)^(1/25) or x = -(-1)^(21/25) (30/7)^(1/25) or x = (-1)^(22/25) (30/7)^(1/25) or x = -(-1)^(23/25) (30/7)^(1/25) or x = (-1)^(24/25) (30/7)^(1/25)
