Find the Product (3a^2b^7)(5a^3b^8)

$(3 a^{2} b^{7}) (5 a^{3} b^{8})$

Step 1

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

Move $a^{3}$ .

$3 (a^{3} a^{2}) b^{7} (5 b^{8})$

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

$3 a^{3 + 2} b^{7} (5 b^{8})$

Add $3$ and $2$ .

$3 a^{5} b^{7} (5 b^{8})$

Step 2

Multiply $b^{7}$ by $b^{8}$ by adding the exponents.

Move $b^{8}$ .

$3 a^{5} (b^{8} b^{7}) \cdot 5$

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

$3 a^{5} b^{8 + 7} \cdot 5$

Add $8$ and $7$ .

$3 a^{5} b^{15} \cdot 5$

Step 3

Multiply $5$ by $3$ .

$15 a^{5} b^{15}$