Trigonometry Examples

$\frac{1}{{(\sqrt{3 x y})}^{8}}$

Step 1

Rewrite ${\sqrt{3 x y}}^{8}$ as ${(3 x y)}^{4}$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x y}$ as ${(3 x y)}^{\frac{1}{2}}$ .

$\frac{1}{{({(3 x y)}^{\frac{1}{2}})}^{8}}$

Step 1.2

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

$\frac{1}{{(3 x y)}^{\frac{1}{2} \cdot 8}}$

Step 1.3

Combine $\frac{1}{2}$ and $8$ .

$\frac{1}{{(3 x y)}^{\frac{8}{2}}}$

Step 1.4

Cancel the common factor of $8$ and $2$ .

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Step 1.4.1

Factor $2$ out of $8$ .

$\frac{1}{{(3 x y)}^{\frac{2 \cdot 4}{2}}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $2$ out of $2$ .

$\frac{1}{{(3 x y)}^{\frac{2 \cdot 4}{2 (1)}}}$

Step 1.4.2.2

Cancel the common factor.

$\frac{1}{{(3 x y)}^{\frac{2 \cdot 4}{2 \cdot 1}}}$

Step 1.4.2.3

Rewrite the expression.

$\frac{1}{{(3 x y)}^{\frac{4}{1}}}$

Step 1.4.2.4

Divide $4$ by $1$ .

$\frac{1}{{(3 x y)}^{4}}$

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 $3 x y$ .

$\frac{1}{{(3 x)}^{4} y^{4}}$

Step 2.2

Apply the product rule to $3 x$ .

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

Step 3

Raise $3$ to the power of $4$ .

$\frac{1}{81 x^{4} y^{4}}$