Algebra Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $3$ and $\frac{1}{x^{2}}$ .

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $2 x$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

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

$8 \frac{3}{x^{2}} x^{3}$

Step 4

Multiply $8 \frac{3}{x^{2}}$ .

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Step 4.1

Combine $8$ and $\frac{3}{x^{2}}$ .

$\frac{8 \cdot 3}{x^{2}} x^{3}$

Step 4.2

Multiply $8$ by $3$ .

$\frac{24}{x^{2}} x^{3}$

Step 5

Cancel the common factor of $x^{2}$ .

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Step 5.1

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

$\frac{24}{x^{2}} (x^{2} x)$

Step 5.2

Cancel the common factor.

$\frac{24}{x^{2}} (x^{2} x)$

Step 5.3

Rewrite the expression.

$24 x$