To divide indices you subtract, hust like to multiply you add. eg 5 to the sixth divide by 5 to the fourth is five to the (6 - 4) ie 5 squared ie 25.
Check it : 5 to the sixth = 5 x 5 x 5 x 5 x 5 x 5; 5 to the fourth = 5 x 5 x 5 x 5;
To divide 5 x 5 x 5 x 5 cancels out leaving 5 x 5.
Chat with our AI personalities
The infinite series is 1 - x2/2! + x4/4! - x6/6! + ...
w4
I will use the quotient rule here. d/dx(f(x)/g(x) = g(x)*f'(x) - f(x)*g'(x)/[g(x)]2 x3*1/x - ln(x)*3x2/(x3)2 x3/x - 3ln(x)x2/x6 x2 - 3ln(x)x2/x6 = - 3ln(x)/x4 =========
So x4 - 1 is the difference of squares, so x4 - 1 = (x2 - 1)(x2 + 1) = (x + 1)(x - 1)(x2 + 1).
(x - y)(x + y)(x2 - xy + y2)(x2 + xy + y2)