Question

pls answer the question. will mark brainliest​

Answer 1

Answer:

$\green{ \longrightarrow\sf \: \large GIVEN \longleftarrow}$

$\displaystyle \: \sf \: \frac{ \sqrt{ {x}^{3} }. \sqrt[3]{ {x}^{5} } }{ \sqrt[5]{ {x}^{3} } } . \sqrt[30]{ {x}^{77} }$

$\green{ \longrightarrow\sf \: \large TO \: FIND \longleftarrow}$

$\sf \: </p><p>What \: should \: be \: multiply \: to \: get \: 1</p><p>$

$\green{ \longrightarrow\sf \large SOLUTION \longleftarrow}$

$\sf \: First \: simply \: this \: expression$

$\displaystyle \: \sf \: \frac{ \sqrt{ {x}^{3} }. \sqrt[3]{ {x}^{5} } }{ \sqrt[5]{ {x}^{3} } } . \sqrt[30]{ {x}^{77} } \\ \\ = \large \sf \frac{ {x}^{ (\frac{3}{2})} . {x}^{ \frac{5}{3} } }{ {x}^{ \frac{3}{5} } } . {x}^{ \frac{77}{30} } \\ \\ = \sf \: \large{x}^{ (\frac{3}{2} + \frac{5}{3} + \frac{77}{30} - \frac{3}{5} )} \\ \\ = \sf \: \large {x}^{ (\frac{45 + 50 + 77 - 18}{30}) } \\ \\ = \sf \large {x}^{( \frac{154}{30}) } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \large \: = {x}^{ \frac{77}{15} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \sf \large \sqrt[15]{ {x}^{77} } \: \: \: \: \: \: \: \: \: \:$

$\sf \: This \: is \: the \: simplified \: term \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \: let \: z \: be \: multiplied \: so \: \: we \: get \: \: product \: 1$

$\sf \: \large \: \{ \sqrt[15]{ {x}^{77} } \}.z \: = 1 \\ \\ \implies \sf \: \green{ \boxed{ \sf \: z = \frac{1}{ \sqrt[15]{ {x}^{77} } } }}$

So option C is correct.