Simplify 1/3*((2a^3b)(6b^3))

$\frac{1}{3} \cdot ((2 a^{3} b) (6 b^{3}))$

Step 1

Multiply $b$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{1}{3} \cdot (2 a^{3} (b^{3} b) \cdot 6)$

Multiply $b^{3}$ by $b$ .

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

$\frac{1}{3} \cdot (2 a^{3} (b^{3} b^{1}) \cdot 6)$

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

$\frac{1}{3} \cdot (2 a^{3} b^{3 + 1} \cdot 6)$

Add $3$ and $1$ .

$\frac{1}{3} \cdot (2 a^{3} b^{4} \cdot 6)$

Step 2

Multiply $6$ by $2$ .

$\frac{1}{3} \cdot (12 a^{3} b^{4})$

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $12 a^{3} b^{4}$ .

$\frac{1}{3} \cdot (3 (4 a^{3} b^{4}))$

Cancel the common factor.

$\frac{1}{3} \cdot (3 (4 a^{3} b^{4}))$

Rewrite the expression.

$4 a^{3} b^{4}$