Simplify 5m^(n+1)*3m^(2n)

$5 m^{n + 1} \cdot 3 m^{2 n}$

Rewrite using the commutative property of multiplication.

$5 \cdot 3 m^{n + 1} m^{2 n}$

Multiply $m^{n + 1}$ by $m^{2 n}$ by adding the exponents.

Move $m^{2 n}$ .

$5 \cdot 3 (m^{2 n} m^{n + 1})$

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

$5 \cdot 3 m^{2 n + n + 1}$

Add $2 n$ and $n$ .

$5 \cdot 3 m^{3 n + 1}$

Multiply $5$ by $3$ .

$15 m^{3 n + 1}$