Write in Standard Form w^3(3w^2+2w)+5w^4

$w^{3} (3 w^{2} + 2 w) + 5 w^{4}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Simplify each term.

Apply the distributive property.

$w^{3} (3 w^{2}) + w^{3} (2 w) + 5 w^{4}$

Rewrite using the commutative property of multiplication.

$3 w^{3} w^{2} + w^{3} (2 w) + 5 w^{4}$

Rewrite using the commutative property of multiplication.

$3 w^{3} w^{2} + 2 w^{3} w + 5 w^{4}$

Simplify each term.

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

Move $w^{2}$ .

$3 (w^{2} w^{3}) + 2 w^{3} w + 5 w^{4}$

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

$3 w^{2 + 3} + 2 w^{3} w + 5 w^{4}$

Add $2$ and $3$ .

$3 w^{5} + 2 w^{3} w + 5 w^{4}$

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

Move $w$ .

$3 w^{5} + 2 (w \cdot w^{3}) + 5 w^{4}$

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

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

$3 w^{5} + 2 (w^{1} w^{3}) + 5 w^{4}$

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

$3 w^{5} + 2 w^{1 + 3} + 5 w^{4}$

Add $1$ and $3$ .

$3 w^{5} + 2 w^{4} + 5 w^{4}$

Add $2 w^{4}$ and $5 w^{4}$ .

$3 w^{5} + 7 w^{4}$