Simplify c^4(5c^3+c^5)

$c^{4} (5 c^{3} + c^{5})$

Step 1

Apply the distributive property.

$c^{4} (5 c^{3}) + c^{4} c^{5}$

Step 2

Rewrite using the commutative property of multiplication.

$5 c^{4} c^{3} + c^{4} c^{5}$

Step 3

Multiply $c^{4}$ by $c^{5}$ by adding the exponents.

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

$5 c^{4} c^{3} + c^{4 + 5}$

Add $4$ and $5$ .

$5 c^{4} c^{3} + c^{9}$

Step 4

Multiply $c^{4}$ by $c^{3}$ by adding the exponents.

Move $c^{3}$ .

$5 (c^{3} c^{4}) + c^{9}$

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

$5 c^{3 + 4} + c^{9}$

Add $3$ and $4$ .

$5 c^{7} + c^{9}$