Trigonometry Examples

${(4 x)}^{3} = 9^{6}$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$4 x = \sqrt[3]{9^{6}}$

Step 2

Divide each term in $4 x = \sqrt[3]{9^{6}}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x = \sqrt[3]{9^{6}}$ by $4$ .

$\frac{4 x}{4} = \frac{\sqrt[3]{9^{6}}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\sqrt[3]{9^{6}}}{4}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt[3]{9^{6}}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the numerator.

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Step 2.3.1.1

Raise $9$ to the power of $6$ .

$x = \frac{\sqrt[3]{531441}}{4}$

Step 2.3.1.2

Rewrite $531441$ as $81^{3}$ .

$x = \frac{\sqrt[3]{81^{3}}}{4}$

Step 2.3.1.3

Pull terms out from under the radical, assuming real numbers.

$x = \frac{81}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{81}{4}$

Decimal Form:

$x = 20.25$

Mixed Number Form:

$x = 20 \frac{1}{4}$