Algebra Examples

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

Step 1

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 1.1

Move $x^{2}$ .

$x^{2} x^{3} \cdot - 1 {(2 x)}^{3}$

Step 1.2

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

$x^{2 + 3} \cdot - 1 {(2 x)}^{3}$

Step 1.3

Add $2$ and $3$ .

$x^{5} \cdot - 1 {(2 x)}^{3}$

Step 2

Move $- 1$ to the left of $x^{5}$ .

$- 1 \cdot x^{5} {(2 x)}^{3}$

Step 3

Rewrite $- 1 x^{5}$ as $- x^{5}$ .

$- x^{5} {(2 x)}^{3}$

Step 4

Apply the product rule to $2 x$ .

$- x^{5} (2^{3} x^{3})$

Step 5

Rewrite using the commutative property of multiplication.

$- 1 \cdot 2^{3} x^{5} x^{3}$

Step 6

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Step 6.1

Move $x^{3}$ .

$- 1 \cdot 2^{3} (x^{3} x^{5})$

Step 6.2

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

$- 1 \cdot 2^{3} x^{3 + 5}$

Step 6.3

Add $3$ and $5$ .

$- 1 \cdot 2^{3} x^{8}$

Step 7

Raise $2$ to the power of $3$ .

$- 1 \cdot 8 x^{8}$

Step 8

Multiply $- 1$ by $8$ .

$- 8 x^{8}$