Simplify 5f^2g(-2(fg^3))g^4

$5 f^{2} g (- 2 (f g^{3})) g^{4}$

Step 1

Multiply $f^{2}$ by $f$ by adding the exponents.

Move $f$ .

$5 (f \cdot f^{2}) g (- 2 (g^{3})) g^{4}$

Multiply $f$ by $f^{2}$ .

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

$5 (f^{1} f^{2}) g (- 2 (g^{3})) g^{4}$

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

$5 f^{1 + 2} g (- 2 (g^{3})) g^{4}$

Add $1$ and $2$ .

$5 f^{3} g (- 2 (g^{3})) g^{4}$

Step 2

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

Move $g^{3}$ .

$5 f^{3} (g^{3} g) \cdot - 2 g^{4}$

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

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

$5 f^{3} (g^{3} g^{1}) \cdot - 2 g^{4}$

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

$5 f^{3} g^{3 + 1} \cdot - 2 g^{4}$

Add $3$ and $1$ .

$5 f^{3} g^{4} \cdot - 2 g^{4}$

Step 3

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

Move $g^{4}$ .

$5 f^{3} (g^{4} g^{4}) \cdot - 2$

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

$5 f^{3} g^{4 + 4} \cdot - 2$

Add $4$ and $4$ .

$5 f^{3} g^{8} \cdot - 2$

Step 4

Multiply $- 2$ by $5$ .

$- 10 f^{3} g^{8}$