Trigonometry Examples

$\frac{2}{3 \sqrt[5]{9}}$

Step 1

Multiply $\frac{2}{3 \sqrt[5]{9}}$ by $\frac{{\sqrt[5]{9}}^{4}}{{\sqrt[5]{9}}^{4}}$ .

$\frac{2}{3 \sqrt[5]{9}} \cdot \frac{{\sqrt[5]{9}}^{4}}{{\sqrt[5]{9}}^{4}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{2}{3 \sqrt[5]{9}}$ by $\frac{{\sqrt[5]{9}}^{4}}{{\sqrt[5]{9}}^{4}}$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \sqrt[5]{9} {\sqrt[5]{9}}^{4}}$

Step 2.2

Move $\sqrt[5]{9}$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 (\sqrt[5]{9} {\sqrt[5]{9}}^{4})}$

Step 2.3

Raise $\sqrt[5]{9}$ to the power of $1$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 ({\sqrt[5]{9}}^{1} {\sqrt[5]{9}}^{4})}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 {\sqrt[5]{9}}^{4}}{3 {\sqrt[5]{9}}^{1 + 4}}$

Step 2.5

Add $1$ and $4$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 {\sqrt[5]{9}}^{5}}$

Step 2.6

Rewrite ${\sqrt[5]{9}}^{5}$ as $9$ .

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Step 2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{9}$ as $9^{\frac{1}{5}}$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 {(9^{\frac{1}{5}})}^{5}}$

Step 2.6.2

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

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \cdot 9^{\frac{1}{5} \cdot 5}}$

Step 2.6.3

Combine $\frac{1}{5}$ and $5$ .

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \cdot 9^{\frac{5}{5}}}$

Step 2.6.4

Cancel the common factor of $5$ .

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Step 2.6.4.1

Cancel the common factor.

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \cdot 9^{\frac{5}{5}}}$

Step 2.6.4.2

Rewrite the expression.

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \cdot 9^{1}}$

Step 2.6.5

Evaluate the exponent.

$\frac{2 {\sqrt[5]{9}}^{4}}{3 \cdot 9}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[5]{9}}^{4}$ as $\sqrt[5]{9^{4}}$ .

$\frac{2 \sqrt[5]{9^{4}}}{3 \cdot 9}$

Step 3.2

Raise $9$ to the power of $4$ .

$\frac{2 \sqrt[5]{6561}}{3 \cdot 9}$

Step 3.3

Rewrite $6561$ as $3^{5} \cdot 27$ .

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Step 3.3.1

Factor $243$ out of $6561$ .

$\frac{2 \sqrt[5]{243 (27)}}{3 \cdot 9}$

Step 3.3.2

Rewrite $243$ as $3^{5}$ .

$\frac{2 \sqrt[5]{3^{5} \cdot 27}}{3 \cdot 9}$

Step 3.4

Pull terms out from under the radical.

$\frac{2 \cdot 3 \sqrt[5]{27}}{3 \cdot 9}$

Step 3.5

Multiply $2$ by $3$ .

$\frac{6 \sqrt[5]{27}}{3 \cdot 9}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Multiply $3$ by $9$ .

$\frac{6 \sqrt[5]{27}}{27}$

Step 4.2

Cancel the common factor of $6$ and $27$ .

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Step 4.2.1

Factor $3$ out of $6 \sqrt[5]{27}$ .

$\frac{3 (2 \sqrt[5]{27})}{27}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $3$ out of $27$ .

$\frac{3 (2 \sqrt[5]{27})}{3 (9)}$

Step 4.2.2.2

Cancel the common factor.

$\frac{3 (2 \sqrt[5]{27})}{3 \cdot 9}$

Step 4.2.2.3

Rewrite the expression.

$\frac{2 \sqrt[5]{27}}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt[5]{27}}{9}$

Decimal Form:

$0.42959600 \dots$