Simplify 3n^(-1/2)*3n

$3 n^{- \frac{1}{2}} \cdot 3 n$

Rewrite using the commutative property of multiplication.

$3 \cdot 3 n^{- \frac{1}{2}} n$

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

Move $n$ .

$3 \cdot 3 (n \cdot n^{- \frac{1}{2}})$

Multiply $n$ by $n^{- \frac{1}{2}}$ .

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

$3 \cdot 3 (n^{1} n^{- \frac{1}{2}})$

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

$3 \cdot 3 n^{1 - \frac{1}{2}}$

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

$3 \cdot 3 n^{\frac{2}{2} - \frac{1}{2}}$

Combine the numerators over the common denominator.

$3 \cdot 3 n^{\frac{2 - 1}{2}}$

Subtract $1$ from $2$ .

$3 \cdot 3 n^{\frac{1}{2}}$

Multiply $3$ by $3$ .

$9 n^{\frac{1}{2}}$