Simplify 1/4(3c^4d^9)(8d)

$\frac{1}{4} (3 c^{4} d^{9}) (8 d)$

Step 1

Multiply $d^{9}$ by $d$ by adding the exponents.

Move $d$ .

$\frac{1}{4} \cdot (3 c^{4} (d \cdot d^{9}) \cdot 8)$

Multiply $d$ by $d^{9}$ .

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

$\frac{1}{4} \cdot (3 c^{4} (d^{1} d^{9}) \cdot 8)$

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

$\frac{1}{4} \cdot (3 c^{4} d^{1 + 9} \cdot 8)$

Add $1$ and $9$ .

$\frac{1}{4} \cdot (3 c^{4} d^{10} \cdot 8)$

Step 2

Multiply $8$ by $3$ .

$\frac{1}{4} \cdot (24 c^{4} d^{10})$

Step 3

Cancel the common factor of $4$ .

Factor $4$ out of $24 c^{4} d^{10}$ .

$\frac{1}{4} \cdot (4 (6 c^{4} d^{10}))$

Cancel the common factor.

$\frac{1}{4} \cdot (4 (6 c^{4} d^{10}))$

Rewrite the expression.

$6 c^{4} d^{10}$