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

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

$- 6 n^{2} (9 n^{5}) - 6 n^{2} (7 n^{3})$

Reorder.

Rewrite using the commutative property of multiplication.

$- 6 \cdot 9 n^{2} n^{5} - 6 n^{2} (7 n^{3})$

Rewrite using the commutative property of multiplication.

$- 6 \cdot 9 n^{2} n^{5} - 6 \cdot 7 n^{2} n^{3}$

Step 2

Simplify each term.

Multiply

$n^{2}$ by

$n^{5}$ by adding the exponents.

Move

$n^{5}$ .

$- 6 \cdot 9 (n^{5} n^{2}) - 6 \cdot 7 n^{2} n^{3}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 6 \cdot 9 n^{5 + 2} - 6 \cdot 7 n^{2} n^{3}$

Add

$5$ and

$2$ .

$- 6 \cdot 9 n^{7} - 6 \cdot 7 n^{2} n^{3}$

Multiply

$- 6$ by

$9$ .

$- 54 n^{7} - 6 \cdot 7 n^{2} n^{3}$

Multiply

$n^{2}$ by

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

Move

$n^{3}$ .

$- 54 n^{7} - 6 \cdot 7 (n^{3} n^{2})$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 54 n^{7} - 6 \cdot 7 n^{3 + 2}$

Add

$3$ and

$2$ .

$- 54 n^{7} - 6 \cdot 7 n^{5}$

Multiply

$- 6$ by

$7$ .

$- 54 n^{7} - 42 n^{5}$