Question

Describe how to transform (^6 sqrt x^5)^7 into an expression with a rational exponent.

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ \left(\sqrt[6]{x^5}\right)^7\implies \left( x^{\frac{5}{6}} \right)^7\implies x^{\frac{5}{6}\cdot 7} \implies x^{\frac{5\cdot 7}{6}}\implies x^{\frac{35}{6}}$