# Calculate: 27sqrt(x)=(1)/(x)

## Expression: $27\sqrt{ x }=\frac{ 1 }{ x }$

Multiply both sides of the equation by $x$

$27x\sqrt{ x }=1$

Square both sides of the equation

$729{x}^{2} \times x=1$

Calculate the product

$729{x}^{3}=1$

Divide both sides of the equation by $729$

${x}^{3}=\frac{ 1 }{ 729 }$

Take the root of both sides of the equation

$x=\frac{ 1 }{ 9 }$

Check if the given value is the solution of the equation

$27\sqrt{ \frac{ 1 }{ 9 } }=\frac{ 1 }{ \frac{ 1 }{ 9 } }$

Simplify the expression

$9=9$

The equality is true, therefore $x=\frac{ 1 }{ 9 }$ is a solution of the equation

\begin{align*}&x=\frac{ 1 }{ 9 } \\&\begin{array} { l }x=0.\overset{ \cdot }{ 1 } ,& x={3}^{-2}\end{array}\end{align*}

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