Algebra Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $- 3 x y$ .

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

Step 1.2

Apply the product rule to $- 3 x$ .

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

Step 2

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

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Step 2.1

Move $x^{3}$ .

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

Step 2.2

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

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

Step 2.3

Add $3$ and $4$ .

$2 x^{7} ({(- 3)}^{3} y^{3})$

Step 3

Rewrite using the commutative property of multiplication.

$2 \cdot {(- 3)}^{3} x^{7} y^{3}$

Step 4

Raise $- 3$ to the power of $3$ .

$2 \cdot - 27 x^{7} y^{3}$

Step 5

Multiply $2$ by $- 27$ .

$- 54 x^{7} y^{3}$