Algebra Examples

${(- 4 x^{3})}^{2} \cdot 3 x^{- 2}$

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Apply the product rule to $- 4 x^{3}$ .

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

Step 3

Raise $- 4$ to the power of $2$ .

$3 (16 {(x^{3})}^{2}) x^{- 2}$

Step 4

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 (16 x^{3 \cdot 2}) x^{- 2}$

Step 4.2

Multiply $3$ by $2$ .

$3 (16 x^{6}) x^{- 2}$

Step 5

Multiply $x^{6}$ by $x^{- 2}$ by adding the exponents.

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Step 5.1

Move $x^{- 2}$ .

$3 (16 (x^{- 2} x^{6}))$

Step 5.2

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

$3 (16 x^{- 2 + 6})$

Step 5.3

Add $- 2$ and $6$ .

$3 (16 x^{4})$

Step 6

Multiply $16$ by $3$ .

$48 x^{4}$