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In the given question we have to simplify each expression:

$鈸�{\left(\frac{鈭�2}{q}\right)}^3鈸�{\left(\frac{w}{x}\right)}^{鈭�4}鈸�{\left(\frac{x{y}^3}{3z^2}\right)}^2鈸�{\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3$

Use Quotient to a Power Property, ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

${\left(\frac{鈭�2}{q}\right)}^3=\frac{{(鈭�2)}^3}{{\left(q\right)}^3}$

Simplify.

${\left(\frac{鈭�2}{q}\right)}^3=\frac{鈭�8}{q^3}$

Raise the numerator and denominator to the power.

${\left(\frac{w}{x}\right)}^{鈭�4}=\frac{w^{鈭�4}}{x^{鈭�4}}$

Use the definition of negative exponent.

${\left(\frac{w}{x}\right)}^{鈭�4}=\frac{x^4}{1}路\frac{1}{w^4}$

Multiply.

role="math" localid="1644825006682" ${\left(\frac{w}{x}\right)}^{鈭�4}=\frac{x^4}{w^4}$

Use Quotient to a Power Property, ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

${\left(\frac{x{y}^3}{3z^2}\right)}^2=\frac{x^2{\left(y^3\right)}^2}{{\left(3\right)}^2{\left(z^2\right)}^2}$

Use the Product to a Power Property, ${\left(ab\right)}^m=a^m{b}^m$

${\left(\frac{x{y}^3}{3z^2}\right)}^2=\frac{x^2\left(y^{3路2}\right)}{9(z^{2路2})}$

${\left(\frac{x{y}^3}{3z^2}\right)}^2=\frac{x^2{y}^6}{9z^4}$

Use Quotient to a Power Property, ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

${\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3=\frac{{\left(2\right)}^3{\left(m^{鈭�2}\right)}^3}{{\left(n^{鈭�2}\right)}^3}$

Use the Product to a Power Property, ${\left(ab\right)}^m=a^m{b}^m$

${\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3=\frac{{\left(2\right)}^3\left(m^{鈭�2路3}\right)}{\left(n^{鈭�2路3}\right)}$

${\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3=\frac{8m^{鈭�6}}{n^{鈭�6}}$

Use the definition of negative exponent.

${\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3=\frac{8n^6}{1}路\frac{1}{m^6}$

Simplify.

${\left(\frac{2m^{鈭�2}}{n^{鈭�2}}\right)}^3=\frac{8n^6}{m^6}$