Simplify 8c^2d*10c^3d^5

$8 c^{2} d \cdot 10 c^{3} d^{5}$

Step 1

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

Move $c^{3}$ .

$8 (c^{3} c^{2}) d \cdot (10 d^{5})$

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

$8 c^{3 + 2} d \cdot (10 d^{5})$

Add $3$ and $2$ .

$8 c^{5} d \cdot (10 d^{5})$

Step 2

Multiply $d$ by $d^{5}$ by adding the exponents.

Move $d^{5}$ .

$8 c^{5} (d^{5} d) \cdot 10$

Multiply $d^{5}$ by $d$ .

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

$8 c^{5} (d^{5} d^{1}) \cdot 10$

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

$8 c^{5} d^{5 + 1} \cdot 10$

Add $5$ and $1$ .

$8 c^{5} d^{6} \cdot 10$

Step 3

Multiply $10$ by $8$ .

$80 c^{5} d^{6}$