Simplify m^3n^2(7m^5+2mn^3)

$m^{3} n^{2} (7 m^{5} + 2 m n^{3})$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$m^{3} n^{2} (7 m^{5}) + m^{3} n^{2} (2 m n^{3})$

Reorder.

Rewrite using the commutative property of multiplication.

$7 m^{3} n^{2} m^{5} + m^{3} n^{2} (2 m n^{3})$

Rewrite using the commutative property of multiplication.

$7 m^{3} n^{2} m^{5} + 2 m^{3} n^{2} (m n^{3})$

Step 2

Simplify each term.

Multiply $m^{3}$ by $m^{5}$ by adding the exponents.

Move $m^{5}$ .

$7 (m^{5} m^{3}) n^{2} + 2 m^{3} n^{2} (m n^{3})$

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

$7 m^{5 + 3} n^{2} + 2 m^{3} n^{2} (m n^{3})$

Add $5$ and $3$ .

$7 m^{8} n^{2} + 2 m^{3} n^{2} (m n^{3})$

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

Move $m$ .

$7 m^{8} n^{2} + 2 (m \cdot m^{3}) n^{2} n^{3}$

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

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

$7 m^{8} n^{2} + 2 (m^{1} m^{3}) n^{2} n^{3}$

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

$7 m^{8} n^{2} + 2 m^{1 + 3} n^{2} n^{3}$

Add $1$ and $3$ .

$7 m^{8} n^{2} + 2 m^{4} n^{2} n^{3}$

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

Move $n^{3}$ .

$7 m^{8} n^{2} + 2 m^{4} (n^{3} n^{2})$

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

$7 m^{8} n^{2} + 2 m^{4} n^{3 + 2}$

Add $3$ and $2$ .

$7 m^{8} n^{2} + 2 m^{4} n^{5}$