Algebra Examples

$\frac{{(2 x)}^{3}}{2 x^{3}} \cdot 4 x^{5}$

Step 1

Rewrite using the commutative property of multiplication.

$4 \frac{{(2 x)}^{3}}{2 x^{3}} x^{5}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4$ .

$2 (2) \frac{{(2 x)}^{3}}{2 x^{3}} x^{5}$

Step 2.2

Factor $2$ out of $2 x^{3}$ .

$2 (2) \frac{{(2 x)}^{3}}{2 (x^{3})} x^{5}$

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

$2 \frac{{(2 x)}^{3}}{x^{3}} x^{5}$

Step 3

Combine $2$ and $\frac{{(2 x)}^{3}}{x^{3}}$ .

$\frac{2 {(2 x)}^{3}}{x^{3}} x^{5}$

Step 4

Cancel the common factor of $x^{3}$ .

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Step 4.1

Factor $x^{3}$ out of $x^{5}$ .

$\frac{2 {(2 x)}^{3}}{x^{3}} (x^{3} x^{2})$

Step 4.2

Cancel the common factor.

$\frac{2 {(2 x)}^{3}}{x^{3}} (x^{3} x^{2})$

Step 4.3

Rewrite the expression.

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

Step 5

Apply the product rule to $2 x$ .

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

Step 6

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

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Step 6.1

Move $2^{3}$ .

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

Step 6.2

Multiply $2^{3}$ by $2$ .

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Step 6.2.1

Raise $2$ to the power of $1$ .

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

Step 6.2.2

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

$2^{3 + 1} x^{3} x^{2}$

Step 6.3

Add $3$ and $1$ .

$2^{4} x^{3} x^{2}$

Step 7

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

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Step 7.1

Move $x^{2}$ .

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

Step 7.2

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

$2^{4} x^{2 + 3}$

Step 7.3

Add $2$ and $3$ .

$2^{4} x^{5}$

Step 8

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

$16 x^{5}$