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What is x to the negative 1 power times x to the negative 1 power?
x^-1 * x^-1 =x^(-1 + -1) =x^-2 or alternatively: 1/x times 1/x =1/x^2 (1/x^2) is the same as (x^-2)
How do you multiply negative exponents?
By addition. Exponents are multiplied by adding them together. Example: 22 = 4 = (2x2) 23 = 8= (2x2x2) If we multiply 22 x 23 we get (2x2) x (2x2x2) = 4 x 8 = 32 or 22 x 23 = 25 = (2x2) x (2x2x2) = (2x2x2x2x2) = 25 = 32 Same with negative exponents: (A negative exponent indicates a reciprocal (1/x)) 2-2 = 1/4 (1/2 x 1/2) 2-3 = 1/8 (1/2 x 1/2 x 1/2) 2-2 x 2-3 = 1/4 x 1/8 = 1/32 2-2 x 2-3 = (1/2 x 1/2) x (1/2 x 1/2 x 1/2) = (1/2 x 1/2 x 1/2 x 1/2 x 1/2) = 2(-2)+(-3) = 2-5 = 32 Hope this helps.
Simplify by dividing x3 plus 2x2 plus 3x-6 over x-1?
(x^3 + 2x^2 + 3x - 6)/(x - 1) add and subtract x^2, and write -6 as (- 3) + (-3) = (x^3 - x^2 + x^2 + 2x^2 - 3 + 3x - 3)/(x - 1) = [(x^3 - x^2) + (3x^2 - 3) + (3x - 3)]/(x - 1) = [x^2(x - 1) + 3(x^2 - 1) + 3(x - 1)]/(x - 1) = [x^2(x - 1) + 3(x - 1)(x + 1) + 3(x - 1)]/(x - 1) = [(x - 1)(x^2 + 3x + 3 + 3)]/(x - 1) = x^2 + 3x + 6
How do you factor the expression x cubed minus x squared plus x minus 1?
x^3 - x^2 + x - 1 = (x^3 - x^2) + (x - 1) = x^2(x - 1) + (x - 1) = (x -1)(x^2 + 1)
What is the derivative of the square root of 4-x?
Use the chain rule:d/dx √(4 - x) = d/dx (4 - x)1/2= 1/2 (4 - x)-1/2 x d/dx (4 - x)= 1/2 (4 - x)-1/2 x -1= -1/2 (4 - x)-1/2 or -1/2√(4 - x)
