Simplify (y^(1/2)z^(1/3))(yz)

$(y^{\frac{1}{2}} z^{\frac{1}{3}}) (y z)$

Multiply $y^{\frac{1}{2}}$ by $y$ by adding the exponents.

Move $y$ .

$y \cdot y^{\frac{1}{2}} z^{\frac{1}{3}} z$

Multiply $y$ by $y^{\frac{1}{2}}$ .

Raise $y$ to the power of $1$ .

$y^{1} y^{\frac{1}{2}} z^{\frac{1}{3}} z$

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

$y^{1 + \frac{1}{2}} z^{\frac{1}{3}} z$

Write $1$ as a fraction with a common denominator.

$y^{\frac{2}{2} + \frac{1}{2}} z^{\frac{1}{3}} z$

Combine the numerators over the common denominator.

$y^{\frac{2 + 1}{2}} z^{\frac{1}{3}} z$

Add $2$ and $1$ .

$y^{\frac{3}{2}} z^{\frac{1}{3}} z$

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

Move $z$ .

$y^{\frac{3}{2}} (z \cdot z^{\frac{1}{3}})$

Multiply $z$ by $z^{\frac{1}{3}}$ .

Raise $z$ to the power of $1$ .

$y^{\frac{3}{2}} (z^{1} z^{\frac{1}{3}})$

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

$y^{\frac{3}{2}} z^{1 + \frac{1}{3}}$

Write $1$ as a fraction with a common denominator.

$y^{\frac{3}{2}} z^{\frac{3}{3} + \frac{1}{3}}$

Combine the numerators over the common denominator.

$y^{\frac{3}{2}} z^{\frac{3 + 1}{3}}$

Add $3$ and $1$ .

$y^{\frac{3}{2}} z^{\frac{4}{3}}$