Evaluate: (3x^4y)/(27x^8y)

Expression: $x=\left( \sqrt{ 4 } \times {10}^{-6} \right) \times \left( \sqrt{ 8.1 } \times {10}^{5} \right)\sqrt{ 0.0016 }$

Evaluate the square root

$x=\left( 2 \times {10}^{-6} \right) \times \left( \sqrt{ 8.1 } \times {10}^{5} \right)\sqrt{ 0.0016 }$

Convert the decimal into a fraction

$x=\left( 2 \times {10}^{-6} \right) \times \left( \sqrt{ \frac{ 81 }{ 10 } } \times {10}^{5} \right)\sqrt{ 0.0016 }$

Convert the decimal into a fraction

$x=\left( 2 \times {10}^{-6} \right) \times \left( \sqrt{ \frac{ 81 }{ 10 } } \times {10}^{5} \right)\sqrt{ \frac{ 1 }{ 625 } }$

Remove unnecessary parentheses

$x=2 \times {10}^{-6} \times \left( \sqrt{ \frac{ 81 }{ 10 } } \times {10}^{5} \right)\sqrt{ \frac{ 1 }{ 625 } }$

Remove unnecessary parentheses

$x=2 \times {10}^{-6} \times \sqrt{ \frac{ 81 }{ 10 } } \times {10}^{5} \times \sqrt{ \frac{ 1 }{ 625 } }$

Evaluate the square root

$x=2 \times {10}^{-6} \times \sqrt{ \frac{ 81 }{ 10 } } \times {10}^{5} \times \frac{ 1 }{ 25 }$

To take a root of a fraction, take the root of the numerator and denominator separately

$x=2 \times {10}^{-6} \times \frac{ 9 }{ \sqrt{ 10 } } \times {10}^{5} \times \frac{ 1 }{ 25 }$

Calculate the product

$x=\frac{ 18 \times {10}^{-1} }{ 25\sqrt{ 10 } }$

If a negative exponent is in the numerator, move the expression to the denominator and make the exponent positive

$x=\frac{ 18 }{ 25\sqrt{ 10 } \times 10 }$

Cancel out the common factor $2$

$x=\frac{ 9 }{ 25\sqrt{ 10 } \times 5 }$

Calculate the product

$x=\frac{ 9 }{ 125\sqrt{ 10 } }$

Rationalize the denominator

$\begin{align*}&x=\frac{ 9\sqrt{ 10 } }{ 1250 } \\&x\approx0.0227684\end{align*}$