Precalculus Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $1$ as $1^{3}$ .

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

Step 2.2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 1$ .

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

Step 2.3

Simplify.

Tap for more steps...

Step 2.3.1

Multiply $x$ by $1$ .

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

Step 2.3.2

One to any power is one.

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

Step 2.4

Apply the product rule to $(x - 1) (x^{2} + x + 1)$ .

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