Algebra Examples

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

Step 1

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

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Step 1.1

Move $a^{4}$ .

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

Step 1.2

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

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

Step 1.3

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.

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Step 4.1

Move $a^{2}$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.3

Add $2$ and $1$ .

$3 \cdot 2 a^{3}$

Step 5

Multiply $3$ by $2$ .

$6 a^{3}$