The answer is: z² . __________________________ Given: <span>(x÷(y÷z))÷((x÷y)÷z) ; without any specified values for the variables; _______________________ we shall simplify. ___________________ We have: __________ </span>(x÷(y÷z)) / ((x÷y)÷z) . _____________________________________ Start with the first term; or, "numerator": (x÷(y÷z)) ; _____________________________________ x ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) = [(xz) / y ] _____________________________________ Then, take the second term; or "denominator": _____________________________________ ((x ÷ y) ÷z ) = (x / y) / z = (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)] _________________________________________ So (x÷(y÷z)) / ((x÷y)÷z) = (x÷(y÷z)) ÷ ((x÷y)÷z) =
[(xz) / y ] ÷ [x / (zy)] = [(xz) / y ] / [x / (zy)] = [(xz) / y ] * [(zy) / x] ; _______________________________________ The 2 (two) z's "cancel out" to "1" ; and The 2 (two) y's = "cancel out" to "1" ; ______________________________________________ And we are left with: z * z = z² . The answer is: z² . ______________________________________________