Trigonometry Examples

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

Step 1

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

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

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

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

Step 2.2

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

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

Step 3

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.2

Multiply $2$ by $3$ .

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

Step 4

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

$\frac{x^{3} y^{6}}{27}$