Convert to Radical Form (m^(1/3)n^(7/3))^(3/4)

${(m^{\frac{1}{3}} n^{\frac{7}{3}})}^{\frac{3}{4}}$

Step 1

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

${(\sqrt[3]{m^{1}} n^{\frac{7}{3}})}^{\frac{3}{4}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

${(\sqrt[3]{m^{1}} \sqrt[3]{n^{7}})}^{\frac{3}{4}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[4]{{(\sqrt[3]{m^{1}} \sqrt[3]{n^{7}})}^{3}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt[4]{{(\sqrt[3]{m} \sqrt[3]{n^{7}})}^{3}}$