Question

${(x \sqrt{x}) }^{x} = {x}^{x \sqrt{x} }$
find the value of x​

Answer 1

Please refer the above picture...

Hope it is helpful to you.

Please mark my answer as brainliest...

Answer 2

$\huge{\mathcal\pink{{ANSWER}}}$

${(x \sqrt{x} )}^{x} = {x}^{x \sqrt{x} }$

as we know that the value of square root is power 1/2

${(x. {x}^{ \frac{1}{2} } )}^{x} = {x}^{x. {x}^{ \frac{1}{2} } }$

bases are same powers should be added

${( {x}^{1 + \frac{1}{2} }) }^{x} = {x}^{ {x}^{1 + \frac{1}{2} } } \\ {( {x}^{ \frac{3}{2} } )}^{x} = {x}^{ {x}^{ \frac{3}{2} } } \\ {x}^{ \frac{3}{2}x } = {x}^{ {x}^{ \frac{3}{2} } }$

bases are same powers should be equated

$\frac{3}{2} x = {x}^{ \frac{3}{2} } \\ \frac{3}{2} = \frac{ {x}^{ \frac{3}{2} } }{x} \\ \frac{3}{2} = {x}^{ \frac{3}{2} } . {x}^{ - 1}$

again bases are same powers should be added

$\frac{3}{2} = {x}^{ \frac{3}{2} - 1} \\ \frac{3}{2} = {x}^{ \frac{1}{2} }$

$\huge{\mathsf\red{S.O.B.S}}$

squaring on both sides

$( { \frac{3}{2} )}^{2} = {( {x}^{ \frac{1}{2} }) }^{2} \\ \frac{9}{4} = x$

$\huge{\boxed{\mathsf\green{ x = \frac{9}{4} }}}$

hope this helps you