Simplify (3a^-3)(a^4)(2a^2)

$(3 a^{- 3}) (a^{4}) (2 a^{2})$

Step 1

Multiply $a^{- 3}$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$3 (a^{4} a^{- 3}) (2 a^{2})$

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

$3 a^{4 - 3} (2 a^{2})$

Subtract $3$ from $4$ .

$3 a^{1} (2 a^{2})$

Step 2

Simplify $3 a^{1} (2 a^{2})$ .

$3 a (2 a^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$3 \cdot 2 a \cdot a^{2}$

Step 4

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

Move $a^{2}$ .

$3 \cdot 2 (a^{2} a)$

Multiply $a^{2}$ by $a$ .

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

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

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

$3 \cdot 2 a^{2 + 1}$

Add $2$ and $1$ .

$3 \cdot 2 a^{3}$

Step 5

Multiply $3$ by $2$ .

$6 a^{3}$