pls help look at the photo thanks

[tex]\displaystyle\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7}*\frac{x*\sqrt{x} }{\sqrt[3]{x^2} } \\\\\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7}*\frac{x*x^\frac{1}{2} }{x^\frac{2}{3} } \\\\\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7} *\frac{x^{1+\frac{1}{2} }}{x^\frac{2}{3} } \\\\\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7}*\frac{x^\frac{3}{2} }{x^\frac{2}{3} }\\ \\\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7}*x^{\frac{3}{2}-\frac{2}{3}}\\ \\\\\f[/tex]

[tex]\displaystyle\\\frac{2x*\sqrt{x} }{7\sqrt[3]{x^2} } =\frac{2}{7} x^\frac{5}{6} .[/tex]

dashataran dashataran · Answer 2 · 2024-02-13T12:23:04+01:00

Answer:

[tex]\dfrac{2}{7}x^{\frac{5}{6}}[/tex]

Step-by-step explanation:

[tex]\dfrac{2x\times\sqrt x}{7\sqrt[3]{x^2}}\\\\=\dfrac{2x\times x^{\frac{1}{2}}}{7\times x^{\frac{2}{3}}}\\\\=\dfrac{2\times x^{1+\frac{1}{2}}}{7x^{\frac{2}{3}}}\\\\=\dfrac{2x^{\frac{3}{2}}}{7x^\frac{2}{3}}\\[/tex]

[tex]=\dfrac{2}{7}x^{\frac{3}{2}-\frac{2}{3}}\\\\=\dfrac{2}{7}x^{\frac{5}{6}}[/tex]

Laws of indices:

[tex]\text{1. }a^m\times a^n=a^{m+n}\\\\\text{2. }a^m\div a^n=a^{m-n}[/tex]