To calculate: To evaluate the expression (27x^{6}y^{3})^{-2/3}.

To calculate:
To evaluate the expression ${\left(27{x}^{6}{y}^{3}\right)}^{-\frac{2}{3}}$.
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Calculation:
Applying the fraction rule, $\frac{-a}{b}=-\frac{a}{b}$
The expression can be written as ${\left(27{x}^{6}{y}^{3}\right)}^{-\frac{2}{3}}$
According to the basic rules of exponents, ${a}^{-m}=\frac{1}{{a}^{m}}$
Applying the above rule,
This can be written as $\frac{1}{{\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}}$
${\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}={27}^{\frac{2}{3}}{\left({x}^{6}\right)}^{\frac{2}{3}}{\left({y}^{3}\right)}^{\frac{2}{3}}$ (According to exponent rule, ${\left(a\cdot b\right)}^{n}={a}^{n}{b}^{n}\right)$
$\frac{1}{{\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}}=\frac{1}{{27}^{\frac{2}{3}}{\left({x}^{6}\right)}^{\frac{2}{3}}{\left({y}^{3}\right)}^{\frac{2}{3}}}$
$\frac{1}{{\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}}=\frac{1}{{\left({3}^{3}\right)}^{\frac{2}{3}}{\left({x}^{6}\right)}^{\frac{2}{3}}{\left({y}^{3}\right)}^{\frac{2}{3}}}$
$\frac{1}{{\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}}=\frac{1}{{\left(3\right)}^{3×\frac{2}{3}}{\left(x\right)}^{6×\frac{2}{3}}{\left(y\right)}^{3×\frac{2}{3}}}$
$\frac{1}{{\left(27{x}^{6}{y}^{3}\right)}^{\frac{2}{3}}}=\frac{1}{9{x}^{4}{y}^{2}}$