Simplify (3n^(1/5))(9n^(4/5))

$(3 n^{\frac{1}{5}}) (9 n^{\frac{4}{5}})$

Rewrite using the commutative property of multiplication.

$3 \cdot 9 n^{\frac{1}{5}} n^{\frac{4}{5}}$

Multiply $n^{\frac{1}{5}}$ by $n^{\frac{4}{5}}$ by adding the exponents.

Move $n^{\frac{4}{5}}$ .

$3 \cdot 9 (n^{\frac{4}{5}} n^{\frac{1}{5}})$

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

$3 \cdot 9 n^{\frac{4}{5} + \frac{1}{5}}$

Combine the numerators over the common denominator.

$3 \cdot 9 n^{\frac{4 + 1}{5}}$

Add $4$ and $1$ .

$3 \cdot 9 n^{\frac{5}{5}}$

Divide $5$ by $5$ .

$3 \cdot 9 n^{1}$

Simplify $3 \cdot 9 n^{1}$ .

$3 \cdot 9 n$

Multiply $3$ by $9$ .

$27 n$