Simplify (m^(2/3)n^(-1/3))^6

${(m^{\frac{2}{3}} n^{- \frac{1}{3}})}^{6}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(m^{\frac{2}{3}} \frac{1}{n^{\frac{1}{3}}})}^{6}$

Combine $m^{\frac{2}{3}}$ and $\frac{1}{n^{\frac{1}{3}}}$ .

${(\frac{m^{\frac{2}{3}}}{n^{\frac{1}{3}}})}^{6}$

Apply basic rules of exponents.

Apply the product rule to $\frac{m^{\frac{2}{3}}}{n^{\frac{1}{3}}}$ .

$\frac{{(m^{\frac{2}{3}})}^{6}}{{(n^{\frac{1}{3}})}^{6}}$

Multiply the exponents in ${(m^{\frac{2}{3}})}^{6}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{\frac{2}{3} \cdot 6}}{{(n^{\frac{1}{3}})}^{6}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{m^{\frac{2}{3} \cdot (3 (2))}}{{(n^{\frac{1}{3}})}^{6}}$

Cancel the common factor.

$\frac{m^{\frac{2}{3} \cdot (3 \cdot 2)}}{{(n^{\frac{1}{3}})}^{6}}$

Rewrite the expression.

$\frac{m^{2 \cdot 2}}{{(n^{\frac{1}{3}})}^{6}}$

Multiply $2$ by $2$ .

$\frac{m^{4}}{{(n^{\frac{1}{3}})}^{6}}$

Multiply the exponents in ${(n^{\frac{1}{3}})}^{6}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{4}}{n^{\frac{1}{3} \cdot 6}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{m^{4}}{n^{\frac{1}{3} \cdot (3 (2))}}$

Cancel the common factor.

$\frac{m^{4}}{n^{\frac{1}{3} \cdot (3 \cdot 2)}}$

Rewrite the expression.

$\frac{m^{4}}{n^{2}}$