Pre-Algebra Examples

$(4 x^{3}) {(8 x)}^{- 1}$

Step 1

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

$4 x^{3} \frac{1}{8 x}$

Step 2

Cancel the common factor of $4 x$ .

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Step 2.1

Factor $4 x$ out of $4 x^{3}$ .

$4 x (x^{2}) \frac{1}{8 x}$

Step 2.2

Factor $4 x$ out of $8 x$ .

$4 x (x^{2}) \frac{1}{4 x (2)}$

Step 2.3

Cancel the common factor.

$4 x \cdot x^{2} \frac{1}{4 x \cdot 2}$

Step 2.4

Rewrite the expression.

$x^{2} \frac{1}{2}$

Step 3

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

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