Simplify (5m^9)(7m^3n^7)+(2m^2n^6)(m^10n)

$(5 m^{9}) (7 m^{3} n^{7}) + (2 m^{2} n^{6}) (m^{10} n)$

Step 1

Simplify each term.

Multiply $m^{9}$ by $m^{3}$ by adding the exponents.

Move $m^{3}$ .

$5 (m^{3} m^{9}) (7 n^{7}) + (2 m^{2} n^{6}) (m^{10} n)$

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

$5 m^{3 + 9} (7 n^{7}) + (2 m^{2} n^{6}) (m^{10} n)$

Add $3$ and $9$ .

$5 m^{12} (7 n^{7}) + (2 m^{2} n^{6}) (m^{10} n)$

Rewrite using the commutative property of multiplication.

$5 \cdot 7 m^{12} n^{7} + (2 m^{2} n^{6}) (m^{10} n)$

Multiply $5$ by $7$ .

$35 m^{12} n^{7} + (2 m^{2} n^{6}) (m^{10} n)$

Multiply $m^{2}$ by $m^{10}$ by adding the exponents.

Move $m^{10}$ .

$35 m^{12} n^{7} + 2 (m^{10} m^{2}) n^{6} n$

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

$35 m^{12} n^{7} + 2 m^{10 + 2} n^{6} n$

Add $10$ and $2$ .

$35 m^{12} n^{7} + 2 m^{12} n^{6} n$

Multiply $n^{6}$ by $n$ by adding the exponents.

Move $n$ .

$35 m^{12} n^{7} + 2 m^{12} (n \cdot n^{6})$

Multiply $n$ by $n^{6}$ .

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

$35 m^{12} n^{7} + 2 m^{12} (n^{1} n^{6})$

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

$35 m^{12} n^{7} + 2 m^{12} n^{1 + 6}$

Add $1$ and $6$ .

$35 m^{12} n^{7} + 2 m^{12} n^{7}$

Step 2

Add $35 m^{12} n^{7}$ and $2 m^{12} n^{7}$ .

$37 m^{12} n^{7}$