Calculus Examples

$\sqrt{3} = x {(27)}^{\frac{1}{3}}$

Step 1

Rewrite the equation as $x \cdot 27^{\frac{1}{3}} = \sqrt{3}$ .

$x \cdot 27^{\frac{1}{3}} = \sqrt{3}$

Step 2

Divide each term in $x \cdot 27^{\frac{1}{3}} = \sqrt{3}$ by $27^{\frac{1}{3}}$ and simplify.

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Step 2.1

Divide each term in $x \cdot 27^{\frac{1}{3}} = \sqrt{3}$ by $27^{\frac{1}{3}}$ .

$\frac{x \cdot 27^{\frac{1}{3}}}{27^{\frac{1}{3}}} = \frac{\sqrt{3}}{27^{\frac{1}{3}}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{x \cdot 27^{\frac{1}{3}}}{27^{\frac{1}{3}}} = \frac{\sqrt{3}}{27^{\frac{1}{3}}}$

Step 2.2.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{3}}{27^{\frac{1}{3}}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify the denominator.

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Step 2.3.1.1

Rewrite $27$ as $3^{3}$ .

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

Step 2.3.1.2

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

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

Step 2.3.1.3

Cancel the common factor of $3$ .

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Step 2.3.1.3.1

Cancel the common factor.

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

Step 2.3.1.3.2

Rewrite the expression.

$x = \frac{\sqrt{3}}{3^{1}}$

Step 2.3.1.4

Evaluate the exponent.

$x = \frac{\sqrt{3}}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{3}$

Decimal Form:

$x = 0.57735026 \dots$