Describe how to transform ( \sqrt[6]{ {x}^(5) } )^(7) into an expression with a rational exponent. Make sure you respond with complete sentences. Thank you!!

Question

Describe how to transform


`( \sqrt[6]{ {x}^(5) } )^(7)`
into an expression with a rational exponent. Make sure you respond with complete sentences. Thank you!!

Answer 1

`\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt[6]{x^5} \right)^7\implies \sqrt[6]{(x^5)^7}\implies \sqrt[6]{x^(5\cdot 7)}\implies \sqrt[6]{x^(35)}\implies x^{(35)/(6)}`