Simplify (2pq^2r^3)(5q^3r^4s)

$(2 p q^{2} r^{3}) (5 q^{3} r^{4} s)$

Step 1

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

Move $q^{3}$ .

$2 p (q^{3} q^{2}) r^{3} (5 r^{4} s)$

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

$2 p q^{3 + 2} r^{3} (5 r^{4} s)$

Add $3$ and $2$ .

$2 p q^{5} r^{3} (5 r^{4} s)$

Step 2

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

Move $r^{4}$ .

$2 p q^{5} (r^{4} r^{3}) (5 s)$

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

$2 p q^{5} r^{4 + 3} (5 s)$

Add $4$ and $3$ .

$2 p q^{5} r^{7} (5 s)$

Step 3

Multiply $5$ by $2$ .

$10 p q^{5} r^{7} s$