Simplify (1/6a^5)(-3a^2)(4a^7)

$(\frac{1}{6} a^{5}) (- 3 a^{2}) (4 a^{7})$

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

Move $a^{2}$ .

$\frac{1}{6} (a^{2} a^{5}) \cdot - 3 (4 a^{7})$

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

$\frac{1}{6} a^{2 + 5} \cdot - 3 (4 a^{7})$

Add $2$ and $5$ .

$\frac{1}{6} a^{7} \cdot - 3 (4 a^{7})$

Multiply $a^{7}$ by $a^{7}$ by adding the exponents.

Move $a^{7}$ .

$\frac{1}{6} (a^{7} a^{7}) \cdot - 3 \cdot 4$

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

$\frac{1}{6} a^{7 + 7} \cdot - 3 \cdot 4$

Add $7$ and $7$ .

$\frac{1}{6} a^{14} \cdot - 3 \cdot 4$

Combine $\frac{1}{6}$ and $a^{14}$ .

$\frac{a^{14}}{6} \cdot - 3 \cdot 4$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{a^{14}}{3 (2)} \cdot - 3 \cdot 4$

Factor $3$ out of $- 3$ .

$\frac{a^{14}}{3 \cdot 2} \cdot (3 \cdot - 1) \cdot 4$

Cancel the common factor.

$\frac{a^{14}}{3 \cdot 2} \cdot (3 \cdot - 1) \cdot 4$

Rewrite the expression.

$\frac{a^{14}}{2} \cdot - 1 \cdot 4$

Combine $\frac{a^{14}}{2}$ and $- 1$ .

$\frac{a^{14} \cdot - 1}{2} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{a^{14} \cdot - 1}{2} \cdot (2 (2))$

Cancel the common factor.

$\frac{a^{14} \cdot - 1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$a^{14} \cdot - 1 \cdot 2$

Simplify the expression.

Multiply $2$ by $- 1$ .

$a^{14} \cdot - 2$

Move $- 2$ to the left of $a^{14}$ .

$- 2 a^{14}$