Simplify the Radical Expression fourth root of y^(7/3)y^(1/3)

$\sqrt[4]{y^{\frac{7}{3}} y^{\frac{1}{3}}}$

Multiply $y^{\frac{7}{3}}$ by $y^{\frac{1}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{y^{\frac{7}{3} + \frac{1}{3}}}$

Combine the numerators over the common denominator.

$\sqrt[4]{y^{\frac{7 + 1}{3}}}$

Add $7$ and $1$ .

$\sqrt[4]{y^{\frac{8}{3}}}$

Rewrite $y^{\frac{8}{3}}$ as ${(y^{\frac{2}{3}})}^{4}$ .

$\sqrt[4]{{(y^{\frac{2}{3}})}^{4}}$

Pull terms out from under the radical.

$| y^{\frac{2}{3}} |$