Simplify (s^3r^2z^5)(s^2r^2z^2)

$(s^{3} r^{2} z^{5}) (s^{2} r^{2} z^{2})$

Step 1

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

Move $s^{2}$ .

$s^{2} s^{3} r^{2} z^{5} (r^{2} z^{2})$

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

$s^{2 + 3} r^{2} z^{5} (r^{2} z^{2})$

Add $2$ and $3$ .

$s^{5} r^{2} z^{5} (r^{2} z^{2})$

Step 2

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

Move $r^{2}$ .

$s^{5} (r^{2} r^{2}) z^{5} z^{2}$

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

$s^{5} r^{2 + 2} z^{5} z^{2}$

Add $2$ and $2$ .

$s^{5} r^{4} z^{5} z^{2}$

Step 3

Multiply $z^{5}$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$s^{5} r^{4} (z^{2} z^{5})$

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

$s^{5} r^{4} z^{2 + 5}$

Add $2$ and $5$ .

$s^{5} r^{4} z^{7}$