Simplify 7x^2y^3(2x^4y^5+6xy^3)

$7 x^{2} y^{3} (2 x^{4} y^{5} + 6 x y^{3})$

Step 1

Apply the distributive property.

$7 x^{2} y^{3} (2 x^{4} y^{5}) + 7 x^{2} y^{3} (6 x y^{3})$

Step 2

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$7 (x^{4} x^{2}) y^{3} (2 y^{5}) + 7 x^{2} y^{3} (6 x y^{3})$

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

$7 x^{4 + 2} y^{3} (2 y^{5}) + 7 x^{2} y^{3} (6 x y^{3})$

Add $4$ and $2$ .

$7 x^{6} y^{3} (2 y^{5}) + 7 x^{2} y^{3} (6 x y^{3})$

Step 3

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

Move $x$ .

$7 x^{6} y^{3} (2 y^{5}) + 7 (x \cdot x^{2}) y^{3} (6 y^{3})$

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

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

$7 x^{6} y^{3} (2 y^{5}) + 7 (x^{1} x^{2}) y^{3} (6 y^{3})$

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

$7 x^{6} y^{3} (2 y^{5}) + 7 x^{1 + 2} y^{3} (6 y^{3})$

Add $1$ and $2$ .

$7 x^{6} y^{3} (2 y^{5}) + 7 x^{3} y^{3} (6 y^{3})$

Step 4

Simplify each term.

Multiply $y^{3}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$7 x^{6} (y^{5} y^{3}) \cdot 2 + 7 x^{3} y^{3} (6 y^{3})$

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

$7 x^{6} y^{5 + 3} \cdot 2 + 7 x^{3} y^{3} (6 y^{3})$

Add $5$ and $3$ .

$7 x^{6} y^{8} \cdot 2 + 7 x^{3} y^{3} (6 y^{3})$

Multiply $2$ by $7$ .

$14 x^{6} y^{8} + 7 x^{3} y^{3} (6 y^{3})$

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

Move $y^{3}$ .

$14 x^{6} y^{8} + 7 x^{3} (y^{3} y^{3}) \cdot 6$

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

$14 x^{6} y^{8} + 7 x^{3} y^{3 + 3} \cdot 6$

Add $3$ and $3$ .

$14 x^{6} y^{8} + 7 x^{3} y^{6} \cdot 6$

Multiply $6$ by $7$ .

$14 x^{6} y^{8} + 42 x^{3} y^{6}$