Question

Please help I'm struggling!

Answer 1

`\sqrt[4]{567x^9 y^(11)} ~~ \begin{cases} 567=3\cdot 3\cdot 3\cdot 3\cdot 7\\ \qquad ~~ ~ 3^4\cdot 7\\ x^9=x^(4+4+1)\\ \qquad ~x^4\cdot x^4\cdot x\\ y^(11)=y^(4+4+3)\\ \qquad ~~ y^4\cdot y^4\cdot y^3 \end{cases}\implies \sqrt[4]{3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3}`

`\left( 3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3\right)^{(1)/(4)}\implies 3^{(4)/(4)}\cdot 7^{(1)/(4)}\cdot x^{(4)/(4)}\cdot x^{(4)/(4)}\cdot x^{(1)/(4)}\cdot y^{(4)/(4)}\cdot y^{(4)/(4)}\cdot y^{(3)/(4)}`

`3\cdot 7^{(1)/(4)}\cdot x\cdot x\cdot x^{(1)/(4)}\cdot y\cdot y\cdot y^{(3)/(4)}\implies 3x^2y^2\cdot 7^{(1)/(4)}x^{(1)/(4)} y^{(3)/(4)} \implies 3x^2y^2(7xy^3)^{(1)/(4)} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2y^2\sqrt[4]{7xy^3} \end{array}}~\hfill`