Simplify (ab^(1/4))(a^(3/11)b^(2/4))

$(a b^{\frac{1}{4}}) (a^{\frac{3}{11}} b^{\frac{2}{4}})$

Multiply $a$ by $a^{\frac{3}{11}}$ by adding the exponents.

Move $a^{\frac{3}{11}}$ .

$a^{\frac{3}{11}} a b^{\frac{1}{4}} b^{\frac{2}{4}}$

Multiply $a^{\frac{3}{11}}$ by $a$ .

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

$a^{\frac{3}{11}} a^{1} b^{\frac{1}{4}} b^{\frac{2}{4}}$

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

$a^{\frac{3}{11} + 1} b^{\frac{1}{4}} b^{\frac{2}{4}}$

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

$a^{\frac{3}{11} + \frac{11}{11}} b^{\frac{1}{4}} b^{\frac{2}{4}}$

Combine the numerators over the common denominator.

$a^{\frac{3 + 11}{11}} b^{\frac{1}{4}} b^{\frac{2}{4}}$

Add $3$ and $11$ .

$a^{\frac{14}{11}} b^{\frac{1}{4}} b^{\frac{2}{4}}$

Multiply $b^{\frac{1}{4}}$ by $b^{\frac{2}{4}}$ by adding the exponents.

Move $b^{\frac{2}{4}}$ .

$a^{\frac{14}{11}} (b^{\frac{2}{4}} b^{\frac{1}{4}})$

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

$a^{\frac{14}{11}} b^{\frac{2}{4} + \frac{1}{4}}$

Combine the numerators over the common denominator.

$a^{\frac{14}{11}} b^{\frac{2 + 1}{4}}$

Add $2$ and $1$ .

$a^{\frac{14}{11}} b^{\frac{3}{4}}$