Question

How to simplify the expression

Answer 1

`\bf \cfrac{12(x+y)^3}{9(x+y)}\implies \cfrac{12}{9}\cdot \cfrac{(x+y)(x+y)(x+y)}{(x+y)} \\\\\\ \cfrac{3\cdot 4}{3\cdot 3}\cdot \cfrac{(x+y)(x+y)(x+y)}{(x+y)}\implies \cfrac{4}{3}\cfrac{(x+y)(x+y)}{1}\implies \cfrac{4(x+y)^2}{3}\\\\ -------------------------------\\\\ \cfrac{3x√(x)}{x^{(1)/(2)}}\impliedby recall\to a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)}\qquad thus\quad \cfrac{3x√(x)}{√(x)}`


`\bf 3x\cdot \cfrac{√(x)}{√(x)}\implies 3x\cdot 1\implies 3x\\\\ -------------------------------\\\\ \left( \cfrac{√(2)√(x^3)}{√(x)} \right)^4\impliedby \textit{now, let's distribute the exponent}`


`\bf \left( \cfrac{(√(2))^4(√(x^3))^4}{(√(x))^4} \right)\implies \cfrac{√(2^4)\sqrt{x^(3\cdot 4)}}{√(x^4)}\implies \cfrac{√((2^2)^2)\sqrt{x^(12)}}{√((x^2)^2)}\implies \cfrac{2^2\sqrt{x^(6\cdot 2)}}{x^2} \\\\\\ \cfrac{2^2√((x^6)^2)}{x^2}\implies \cfrac{2^2x^6}{x^2}\implies 4x^6x^(-2)\implies 4x^(6-2)\implies 4x^4`