Algebra Examples

$6 x y {(3 x y)}^{- 2}$

Step 1

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

$6 x y \frac{1}{{(3 x y)}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $3 x y$ .

$6 x y \frac{1}{{(3 x)}^{2} y^{2}}$

Step 2.2

Apply the product rule to $3 x$ .

$6 x y \frac{1}{3^{2} x^{2} y^{2}}$

Step 2.3

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

$6 x y \frac{1}{9 x^{2} y^{2}}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $3 x y$ .

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Step 3.1.1

Factor $3 x y$ out of $6 x y$ .

$3 x y (2) \frac{1}{9 x^{2} y^{2}}$

Step 3.1.2

Factor $3 x y$ out of $9 x^{2} y^{2}$ .

$3 x y (2) \frac{1}{3 x y (3 x y)}$

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

$2 \frac{1}{3 x y}$

Step 3.2

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

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