((1/a) + (1/b))^-1 = a + b ....why is this false ? Makes sense to me.........Lol. But this IS TRUE: ((1/a)(1/b))^-1 =ab Explain please and thank you.
Because (x + y)^n is NOT the same as x^n + y^n but (xy)^n IS the same as x^n y^n Exponentiation is distributive over multiplication and division, but NOT over addition and subtraction (1/a + 1/b)?1 = (b/(ab) + a/(ab))?1 = ((a+b)/(ab))?1 = ab/(a+b) (1/a * 1/b)?1 = (1/a)?1 * (1/b)?1 = a * b
((1/a) + (1/b))^-1 = ((b + a)/ab)^-1 = ab/(a + b), which is clearly not a + b. False Statement! ((1/a)(1/b))^-1 = (1/ab)^-1 = ab. True Statement