Find the Degree ay*(a^3+4y^4)

$a y \cdot (a^{3} + 4 y^{4})$

Simplify and reorder the polynomial.

Apply the distributive property.

$a y a^{3} + a y (4 y^{4})$

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

Move $a^{3}$ .

$a^{3} a y + a y (4 y^{4})$

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

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

$a^{3} a^{1} y + a y (4 y^{4})$

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

$a^{3 + 1} y + a y (4 y^{4})$

Add $3$ and $1$ .

$a^{4} y + a y (4 y^{4})$

Rewrite using the commutative property of multiplication.

$a^{4} y + 4 a y \cdot y^{4}$

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$a^{4} y + 4 a (y^{4} y)$

Multiply $y^{4}$ by $y$ .

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

$a^{4} y + 4 a (y^{4} y^{1})$

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

$a^{4} y + 4 a y^{4 + 1}$

Add $4$ and $1$ .

$a^{4} y + 4 a y^{5}$

The largest exponent is the degree of the polynomial.

$6$