[tex]~~\left(8x^7y^4\right)^{\tfrac 23}\\\\=\left[ \left(8x^7y^4\right)^2 \right]^{\tfrac 13} \\\\=\left(64x^{14}y^8 \right)^{\tfrac 13}\\\\=\left(64 \right)^{\tfrac 13} \cdot \left( x^{14} \right)^{\tfrac 13} \cdot \left(y^8 \right)^{\tfrac 13}\\\\=\left(4^3 \right)^{\tfrac 13} \cdot \left(x^{12}\cdot x^2\right)^{\tfrac 13} \cdot \left(y^6 \cdot y^2 \right)^{\tfrac 13}\\\\=4 x^4 \cdot \left(x^2 \right)^{\tfrac 13} \cdot y^2 \cdot \left(y^2 \right)^{\tfrac 13}\\\\[/tex]
[tex]=4x^4y^2 \left(x^2 y^2 \right)^{\tfrac 13}\\\\=4x^4y^2 \sqrt[3]{x^2 y^2}[/tex]
