We have the following mathematical expression:
[tex]\sqrt[3]{64x^6y^4z^3}[/tex]From which we must find an equivalent expression, To solve this, we must remember a rule of exponents.
[tex]\sqrt[m]{a^n}=a^{\frac{n}{m}}[/tex]with the above rule we will divide all the exponents of the terms inside the root over 3 and also solve the 64 cubic raiz which is:
[tex]\sqrt[3]{64}=4[/tex]Now we simplify the mathematical expression:
[tex]\begin{gathered} \sqrt[3]{64x^6y^4z^3} \\ \sqrt[3]{64\cdot}\sqrt[3]{x^6}\cdot\sqrt[3]{y^4^{}}\cdot\sqrt[]{z^3} \\ 4\cdot x^{\frac{6}{3}}\cdot y^{\frac{4}{3}}\cdot z^{\frac{3}{3}} \\ 4x^2\cdot y^{\frac{4}{3}}\cdot z \end{gathered}[/tex]In conclusion, the answer is:
[tex]4x^2y^{\frac{4}{3}}z[/tex]