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we have the expression
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}[/tex]Remember that
[tex]\frac{75}{40}=\frac{15}{8}=\frac{15}{2^3}[/tex][tex]\frac{a^7}{a^{(13)}}=\frac{1}{a^6}[/tex]substitute
[tex]\sqrt[3]{\frac{75a^7b^4}{40a^{(13)}c^9}}=\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}[/tex]we have that
[tex]2^3a^6c^9=(2a^2c^3)^3[/tex]substitute
[tex]\sqrt[3]{\frac{15b^4}{2^3a^6c^9}}=\frac{\sqrt[3]{15b^4}}{(2a^2c^3)}=b\frac{\sqrt[3]{15b^{}}}{(2a^2c^3)}[/tex]