Precalculus Examples

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

Step 1

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

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

Step 2

Multiply $3 x \frac{1}{y}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Move $3$ to the left of $x$ .

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

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{y}{3 x}$ .

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

Step 5.2

Apply the product rule to $3 x$ .

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

Step 6

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

$3 x^{2} \frac{y^{2}}{9 x^{2}}$

Step 7

Cancel the common factor of $3 x^{2}$ .

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Step 7.1

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

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

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