Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine.

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

Step 5

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

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Step 5.1

Move $x^{2}$ .

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

Step 5.2

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

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

Step 5.3

Add $2$ and $2$ .

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

Step 6

Multiply $3$ by $1$ .

$\frac{3}{x^{4} \cdot 3}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$\frac{3}{x^{4} \cdot 3}$

Step 7.2

Rewrite the expression.

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