Simplify (rn)(rn^3)(n^2)

$(r n) (r n^{3}) (n^{2})$

Step 1

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$r \cdot r n \cdot n^{3} n^{2}$

Multiply $r$ by $r$ .

$r^{2} n \cdot n^{3} n^{2}$

Step 2

Multiply $n$ by $n^{3}$ by adding the exponents.

Move $n^{3}$ .

$r^{2} (n^{3} n) n^{2}$

Multiply $n^{3}$ by $n$ .

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

$r^{2} (n^{3} n^{1}) n^{2}$

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

$r^{2} n^{3 + 1} n^{2}$

Add $3$ and $1$ .

$r^{2} n^{4} n^{2}$

Step 3

Multiply $n^{4}$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$r^{2} (n^{2} n^{4})$

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

$r^{2} n^{2 + 4}$

Add $2$ and $4$ .

$r^{2} n^{6}$