Precalculus Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the product rule to $\frac{x y}{2}$ .

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

Step 2.2

Apply the product rule to $x y$ .

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

Step 3

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

$\frac{x^{3} y^{3}}{8}$